{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "4b7d1bb7-9dc2-441c-be2c-1ee7e8612610",
   "metadata": {},
   "source": [
    "# Theoretical explanation"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b34e7b01-4666-4744-a057-ce9b2f84f1a9",
   "metadata": {},
   "source": [
    "## Elementary case"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4cee7f33-f7af-4c3f-943e-07f0988de119",
   "metadata": {},
   "source": [
    "Here is an elementary case in one plane. We can imagine that instead of laser rotation we have isotropic emission of photons and we simulate by photon. It is important that we have pure Cauchy form in this model. This form is easy to visually confuse with Gaussian."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "90fe73cc-7058-46d7-8920-377e31a3ea87",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "        <iframe\n",
       "            width=\"1400\"\n",
       "            height=\"600\"\n",
       "            src=\"https://www.randomservices.org/random/apps/Cauchy.html\"\n",
       "            frameborder=\"0\"\n",
       "            allowfullscreen\n",
       "            \n",
       "        ></iframe>\n",
       "        "
      ],
      "text/plain": [
       "<IPython.lib.display.IFrame at 0x73d5cc2402e0>"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.display import IFrame; IFrame('https://www.randomservices.org/random/apps/Cauchy.html', width=1400, height=600)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d678b439-2434-4161-a407-abedfd7aeb0b",
   "metadata": {},
   "source": [
    "### Numerical verification on GPU"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "0c8ba556-6f85-4934-b00f-31a0747aeb0e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Device: cuda\n"
     ]
    }
   ],
   "source": [
    "import numpy as np; import torch; from torch.distributions import Cauchy\n",
    "from tqdm.notebook import tqdm\n",
    "a, b = 0.4, 0.7; n, clip, lr, steps, n_boot = 1_000_000, 10000, 0.01, 300, 50\n",
    "device = torch.device('cuda' if torch.cuda.is_available() else 'cpu'); print(f\"Device: {device}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "2d3395d7-4bc9-476d-96c4-2fb2a55eb119",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "87ae8215b7f64b048e1d5d578eb92d2b",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/50 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True: loc=0.4, scale=0.7\n",
      "Est:  loc=0.4001±0.0011, scale=0.7006±0.0010\n",
      "CPU times: user 15.7 s, sys: 357 ms, total: 16.1 s\n",
      "Wall time: 7.87 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "theta = np.random.uniform(-np.pi/2, np.pi/2, n); X_np = (a + b * np.tan(theta))[np.abs(a + b * np.tan(theta)) < clip]\n",
    "def fit(X): \n",
    "    loc = torch.nn.Parameter(torch.tensor(0.0, device=device)); log_scale = torch.nn.Parameter(torch.tensor(0.0, device=device)); opt = torch.optim.Adam([loc, log_scale], lr=lr)\n",
    "    for _ in range(steps): opt.zero_grad(); (-Cauchy(loc, log_scale.exp()).log_prob(X).mean()).backward(); opt.step()\n",
    "    return loc.item(), log_scale.exp().item()\n",
    "loc_est, scale_est = fit(torch.tensor(X_np, device=device, dtype=torch.float32))\n",
    "boots = np.array([fit(torch.tensor(np.random.choice(X_np, len(X_np)), device=device, dtype=torch.float32)) for _ in tqdm(range(n_boot))])\n",
    "print(f\"True: loc={a}, scale={b}\"); print(f\"Est:  loc={loc_est:.4f}±{boots[:,0].std():.4f}, scale={scale_est:.4f}±{boots[:,1].std():.4f}\") "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a412e3d9-2aad-47cc-a0e2-898d48062e2e",
   "metadata": {},
   "source": [
    "## Numerically generalize to two planes"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3e052204-8667-4992-9dbb-b4dfe18965e7",
   "metadata": {},
   "source": [
    "### X and Y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "a31ebaf5-13e3-451d-9420-d1bef2045a2c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "ac83ffbae3004527b6e27d7f86ee95c7",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/50 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "c45ee59d4b6a4e89bac55968bfd320d9",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/50 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X: loc=0.4003±0.0031, scale=0.6995±0.0034\n",
      "Y: loc=0.4012±0.0030, scale=0.7007±0.0030\n",
      "Expected: loc=0.4, scale≈0.7 for both\n",
      "CPU times: user 29.7 s, sys: 278 ms, total: 30 s\n",
      "Wall time: 13.7 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "u = np.random.uniform(0, 1, n); v = np.random.uniform(0, 1, n); theta = np.arccos(1 - u); phi = 2 * np.pi * v; dx = np.sin(theta) * np.cos(phi); dy = np.sin(theta) * np.sin(phi); dz = np.cos(theta)\n",
    "X = a + b * dx / dz; Y = a + b * dy / dz; X_clip = X[np.abs(X) < clip]; Y_clip = Y[np.abs(Y) < clip]\n",
    "def fit(data): \n",
    "    loc = torch.nn.Parameter(torch.tensor(0.0, device=device)); log_scale = torch.nn.Parameter(torch.tensor(0.0, device=device)); opt = torch.optim.Adam([loc, log_scale], lr=lr)\n",
    "    for _ in range(steps): opt.zero_grad(); (-Cauchy(loc, log_scale.exp()).log_prob(data).mean()).backward(); opt.step()\n",
    "    return loc.item(), log_scale.exp().item()\n",
    "X_tensor = torch.tensor(X_clip, device=device, dtype=torch.float32); loc_X, scale_X = fit(X_tensor)\n",
    "boots_X = np.array([fit(torch.tensor(np.random.choice(X_clip, 100000), device=device, dtype=torch.float32)) for _ in tqdm(range(n_boot))])\n",
    "Y_tensor = torch.tensor(Y_clip, device=device, dtype=torch.float32); loc_Y, scale_Y = fit(Y_tensor)\n",
    "boots_Y = np.array([fit(torch.tensor(np.random.choice(Y_clip, 100000), device=device, dtype=torch.float32)) for _ in tqdm(range(n_boot))])\n",
    "print(f\"X: loc={loc_X:.4f}±{boots_X[:,0].std():.4f}, scale={scale_X:.4f}±{boots_X[:,1].std():.4f}\"); print(f\"Y: loc={loc_Y:.4f}±{boots_Y[:,0].std():.4f}, scale={scale_Y:.4f}±{boots_Y[:,1].std():.4f}\")\n",
    "print(f\"Expected: loc={a}, scale≈{b} for both\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7302ce3d-0b9c-4aab-91a7-a1cb4c1bd176",
   "metadata": {},
   "source": [
    "The form and family are preserved."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5902eb8b-28ab-4528-9ba4-d8060ef8b8db",
   "metadata": {},
   "source": [
    "### XY"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "5b46b1a4-d579-4e74-8784-ed1a1e5ddcfe",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "901ccd4acec843749a12844426a22478",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/50 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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iJsR14u677+bJJ59kz549tc5uBlVfTBwcHEhISKixLD4+HrVafcWJB67k+++/Z9KkSXzwwQfmsvLy8hqzYl3tL5eJiYkWvWFJSUmYTCZCQ0OvuF5THvOft+Hs7IzRaGzUX++PHj1a6+QKRqMRqPryciW7du1i0KBB9dpWcnJyneeyKZw5cwadTmfRa9WzZ082bNhAWlqaxReq6mSgPkPoamv30pk6N27cSGBgoPlXdmvo1q0bmzdvrjF8du/evebljbX+tW6rerhYdY93WloaJpOJ559/nueff75G/bCwMP7yl79c1UyNdnZ2BAQEkJiYyOzZsykqKmLmzJl1rteSYvxazzfUPOctzbUcozVjF1r+uRTiash0+UJcJ5ycnPj000+ZOXMmo0ePrrWORqNh2LBhrF692mIIYGZmJl999RX9+vW76nutNBpNjfumPvnkE3MSUc3R0RGgwdMYz58/v0bbgHkmyivtV1Md85+3cc899/DDDz9w7NixGsuzs7NrlNVnuvyjR4+SkZFhMaSnoqKC+fPn061btzp7eqrvL6nPqzHvvyktLSU+Pt7iXrvazsGRI0f46aefGDZsmMVscOPHjwfgs88+s6j/n//8BxsbG/NjDBra7p+tWLGC/fv388ILL1zVTH1btmxh2bJlDV7v3nvvxWg0Wgx51ev1LF26lOjoaIsfCWo7jw1Zv751axtmW1lZyeeff469vT0dO3YEoHPnzqxcubLGq1OnTgQHB7Ny5UoeffTRBp+Tam3btmXXrl18+OGHTJ06lcDAwDrXaUkx3pC/TX3PeVO42tiF+h+jtWIXmvdcCmFt0mMmxHXkcsPo/uyf//wnGzZsoF+/fjzzzDPY2NiwcOFC9Ho977333lVve9SoUXzxxRe4urrSsWNHdu/ezcaNGy2eHQVVvSEA//d//8f999+Pra0to0ePNidsl5OcnMydd97JiBEj2L17N19++SUTJkwgMjKy2Y75z9599102b95MdHQ0jz/+OB07duTixYscOnSIjRs31hhuVdd0+QUFBeZn9QwYMIBJkyZRVlbGf//7X06cOMHWrVvr3KemuP9m3rx55Ofnm3uvfv75Z1JTU4Gq4ayurq7s27ePQYMG8frrr5t7Pe677z7s7e259dZb8fb25sSJEyxatAgHBwfeffddi210796dRx55hCVLlmAwGMzn6bvvvmP69OkWw5jq0+62bdt48803GTZsGB4eHuzZs4elS5cyYsSIek2ikpmZWe8JJu6+++4rxnJ0dDTjxo1j+vTpZGVl0bZtW5YvX05KSkqNRLS289iQ9etb98knn6SwsJDbbruNgIAAMjIy+O9//0t8fDwffPCBudfR09OTMWPG1Dim6h6y2papVKp6PRYCqhKzxYsX06pVK6ZPn15nfWj8GK9PfMO1/23qe84bsk+1aczYbcgxWit2oWHnUojrXrPOCSmEuKw/T5d/JZdOl68oinLo0CFl+PDhipOTk+Lg4KAMGjSoxpTUDZ0uPy8vT5kyZYri6empODk5KcOHD1fi4+OVkJAQZdKkSRZ133rrLSUgIEBRq9V1TtNcPQ3+iRMnlHvvvVdxdnZW3NzclOeee04pKyurUS87O7vWdq7lmOszXb6iKEpmZqby7LPPKkFBQYqtra3i6+urDB48WFm0aFGN/aGO6fJ37NihAMpjjz1mbi84OFgZN26c+REBzSEkJKTO6barz+Prr79uXu/jjz9Wevfurbi7uys2NjaKn5+f8tBDDymJiYm1bqeiokKZOXOmEhISotja2ipt27ZVPvrooxr16tNuUlKSMmzYMMXT01Oxs7NT2rdvr8yaNUvR6/X1OubGnnK8rKxMefnllxVfX1/Fzs5O6dWrl7J27drLbvfP57Eh69e37tdff60MGTJE8fHxUWxsbBQ3NzdlyJAhyurVq+t1fi43XX5RUVGtjzi4nHfffVcBlHfffbde9ZtCfeJbUa79b9OQc17ffapNUzxOoD7HaK3YVZRrj18hricqRanHnM5CCNFEZs6cyRtvvEF2drb5gdQ3gwULFvD0009TUFBwzUMthWgOa9asYdSoURw5cqReD6L+6KOPmDZtGhcvXsTNzc0KeyiEENcXucdMCCGawbFjxwgICJCkTFy3Nm/ezP3331+vpAyqYj4wMFCSMiGEuAy5x0wIIZrB0aNH5aZ1cV2bPXt2g+pfbhZSIYQQVaTHTAghmsGxY8ckMRM3DUVROHHiBJ07d27uXRFCiBZL7jETQgghhBBCiGYmPWZCCCGEEEII0cwkMRNCCCGEEEKIZiaTf9TBZDJx4cIFnJ2dUalUzb07QgghhBBCiGaiKApFRUX4+/ujVjduH5ckZnW4cOECQUFBzb0bQgghhBBCiBbi/PnzBAYGNmqbkpjVwdnZGYCzZ8/SqlWr5t0ZcUMzmUxkZ2fj5eXV6L/ACPFnEmvCWiTWhLVIrAlryc/PJyQkxJwjNCZJzOpQPXzRxcVFHgQrmpTJZKK8vBwXFxe5qIgmJbEmrEViTViLxJqwFpPJBNAktzhJ5AohhBBCCCFEM5PETAghhBBCCCGamSRmQgghhBBCCNHM5B4zIYQQQggrMxqNVFZWNvdu3DBMJhOVlZWUl5fLPWbimmg0GmxsbJrlMVmSmAkhhBBCWFFxcTGpqakoitLcu3LDUBQFk8lEUVGRPHdWXDMHBwf8/PzQarVW3a4kZkIIIYQQVmI0GklNTcXBwQEvLy9JIhqJoigYDIZm6+kQNwZFUaioqCA7O5vk5GTCw8Ot2gMriZkQQgghhJVUVlaiKApeXl7Y29s39+7cMCQxE43F3t4eW1tbzp49S0VFBTqdzmrblkG4QgghhBBWJsmDEC1Xc92nKImZEEIIIYQQQjQzScyEEEIIIYQQopndFIlZcnIygwYNomPHjnTp0oWSkpLm3iUhhBBCCCGEMLspErPJkyfz5ptvcuLECbZu3YqdnV1z75IQQgghxHVj8uTJqFQqVCoVtra2+Pj4MHToUJYsWYLJZKp3O8uWLaNVq1ZNt6NCXMdu+MTs+PHj2Nra0r9/fwDc3d2xsZHJKIUQQgghGmLEiBGkp6eTkpJCbGwsgwYN4i9/+QujRo3CYDA09+4Jcd1r8YnZtm3bGD16NP7+/qhUKlatWlWjzvz58wkNDUWn0xEdHc2+ffvMyxITE3FycmL06NH06NGDd955x4p7L4QQQghxY7Czs8PX15eAgAB69OjB3/72N1avXk1sbCzLli0D4MMPP6RLly44OjoSFBTEM888Q3FxMQBbtmxhypQpFBQUmHvfZs6cCcAXX3xBVFQUzs7O+Pr6MmHCBLKysprpSIVoHi0+MSspKSEyMpL58+fXunzFihVMmzaN119/nUOHDhEZGcnw4cPN/zMbDAa2b9/Ov//9b3bv3s2GDRvYsGGDNQ9BCCGEEKLRpeaVsjk+i9S80mbbh9tvv53IyEh+/PFHoGqa8blz53L8+HGWL1/Ob7/9xquvvgrArbfeypw5c3BxcSE9PZ309HRefvlloOr5bm+99RZHjhxh1apVpKSkMHny5OY6LCGaRYsf0xcTE0NMTMxll3/44Yc8/vjjTJkyBYAFCxbw66+/smTJEl577TUCAgKIiooiKCgIgJEjRxIXF8fQoUNrbU+v16PX683vCwsLATCZTA0aQy1EQ5lMJhRFkTgTTU5iTViLxFpN1eek+nUtTmUUcehcHoqiENDKOg+rrm2f27dvz++//46iKPzlL38xl4eEhPDWW2/x9NNPM3/+fGxtbXFxcUGlUuHj42PRZvX3OICwsDA+/vhjevfuTVFREU5OTg3at2s9r0JU//9Z2/f/pvw8a/GJ2ZVUVFRw8OBBpk+fbi5Tq9UMGTKE3bt3A9CrVy+ysrLIy8vD1dWVbdu28eSTT162zVmzZvHGG2/UKM/OzqaioqLxD0KI/zGZTBQUFKAoSrM92FDcHCTWhLVIrNVUWVmJyWTCYDBc831ZrT3tMRqNtPa0b/J7vKq/oNa2HaPRCFSNUtq0aRPvvfceCQkJFBYWYjAYKC8vp7CwEAcHB/OX2kvbOXToEG+++SZHjx4lLy/PXO/MmTN07Nixzv1TFMW8H/LwbnGtDAYDJpOJ3NxcbG1tLZYVFBQ02Xav68QsJycHo9Fo8asLgI+PD/Hx8QDY2NjwzjvvcNttt6EoCsOGDWPUqFGXbXP69OlMmzbN/L6wsJCgoCC8vLxkFiHRpEwmEyqVCi8vL/kCI5qUxJqwFom1msrLyykqKsLGxuaaJyML8XQmxNO5kfbsytRqNWq1utZ9TkhIoHXr1qSmpjJmzBieeuop3n77bdzd3dmxYwePPfYYJpMJGxsbcxz8uZ2SkhLuuOMOhg8fzpdffomXlxfnzp1jxIgR5vXq69Iv0UJcjepY9fDwQKfTWSzTarVNt90ma7kFqWs45J/Z2dnVOp1+9QeSEE1JpVJJrAmrkFgT1iKxZkmtVpsnvrgee3Yu3efffvuNo0eP8uKLL3Lo0CFMJhMffvih+e/93XffmddTqVTY2dlhNBot2klISCA3N5d3333XfOvJwYMHLdari6Io5nrX43kVLUt13NX22dWUn2XX9aekp6cnGo2GzMxMi/LMzEx8fX2baa+EEEIIIW48er2ejIwM0tLSOHToEO+88w533XUXo0aN4uGHH6Zt27ZUVlbyySefcObMGb744gsWLFhg0UZoaCjFxcVs2rSJnJwcSktLCQ4ORqvVmtf76aefeOutt5rpKIVoPtd1YqbVaunZsyebNm0yl5lMJjZt2kSfPn2acc+EEEIIIW4sa9euxc/Pj9DQUEaMGMHmzZuZO3cuq1evRqPREBkZyYcffsi//vUvOnfuzH//+19mzZpl0catt97KU089xX333YeXlxfvvfceXl5eLFu2jO+++46OHTvy7rvv8v777zfTUQrRfFRKC5+6pri4mKSkJAC6d+/Ohx9+yKBBg3B3dyc4OJgVK1YwadIkFi5cSO/evZkzZw7ffvst8fHxNe49uxqFhYW4urqSl5cn95iJJmUymcjKysLb21uG/IgmJbEmrEViraby8nKSk5MJCwurce+KuHqKomAwGLCxsZGhjOKaXen/0/z8fNzc3CgoKMDFxaVRt9vi7zE7cOAAgwYNMr+vnphj0qRJLFu2jPvuu4/s7GxmzJhBRkYG3bp1Y+3atY2SlAkhhBBCCCGENbT4xGzgwIF1Po/iueee47nnnrPSHgkhhBBCCCFE45JxBUIIIYQQQgjRzCQxE0IIIYQQQohmJomZEEIIIYQQQjQzScyEEEIIIYQQoplJYiaEEEIIIYQQzUwSMyGEEEIIIYRoZpKY1dOqw2mk5pVednlqXimb47MuW6eu5UIIIYQQQoibV4t/jllLcWjnUTxLSzjrrMPR3pZivREney1FFSZa+zpzJqeMo+cLyMty5LSzjja+LgR6OIFaTWp+Gd8fvkB8RhFGxUQ7bxdAoazSyMgu/gCsOZqOr4uOHiFuJOeUkFeix81RS582ngAkZhYT7uNEoJsDqXmlJGYW46yzoajcUOPfS+tVvwcsyqrbvXQ9IYQQQgghhHVJYlZPKYceYPnvoFaqXhrlj/+ufs2NBYfKP9ZZ2xbWt/ljuZupqjxfUaFWQIWKXxQVgcVqXjpqiwIoajXtVGp+CjeQ5gCrUKFRVNiYVJxFg61KhcmoQqWosVHZ4F+iw71Uh4tKTaVKg85Ww5kAFXmO9mQXGtHrIVFjR7LKBsVkQyUayhU1cRob7HRaFI0NFY46DKg5bIJ4R3v0ahvsnBwx2tqSqVcoUdlSqtJQhAaNgz1qOx2VNrZU2tphsLGlGA1lGhu8vVwpQ0OhSQMqFeWVRoorDHg62dHRryoZTckpobTCRHmlkUqTiSB3ByoqjYCKUE9HXO1tOJ9XSnJOCWGeTgS52ePmqMXJzpZfjlygoLySEZ18sbPVmJPXME8nDp3NI6OwjJFd/IkKdTf/DWpLToUQQgghhGhpJDGrpwoNKHWcLZVi+T7XHhLda6upWPxbkmPEUV9pUSPOBxI86t6vB47BbWf/eF9qC9N7/u+Ncy37CNgZwM4I/9gKEbl/LDvpCT90rFpub6hKMh0qwfV//1aXOVZYrlebUls7Sm3tKbW1o1yrQ69zoMzWjihbHaU2dhTb6ii11VFhp6Ncq6NUa0+ZvQMF9k5kaXSU2zhw2MmZQ61aYXByplKlIatYT6XRxKmsIpy1NugNJnS2arQaDRdL9ZRXmth2KpsgN0fzfhTpKykoq0RRwMvZDp2NBgAHrQZ3Jy36SiNezjpc7W3MPZSSwAkhhBBNT1EUnnzySb7//nvy8vI4fPgwkZGRNcq6devWZNt74YUX6NatG3PmzGmUbSxbtoz33nuPlJQUQkJCeP/997njjjsapW1x45PErJ6cdYEoGgVFpaAoJkwoGFBQqRRMKKBSONOlLaZyE5WVBjCZSPG6SJFDPmoVaFQqQEFRFFCqEiS1CowmE4UOtmQEeqBSFDAasdWoKHbOpdLOgElRQFFQAaCYkz+1YgJFQUGFQQ02JiMAhjruGlSAcpuql/qSRDLbEfYG1H0u7A3w7XeWZYt6wu5AcNGDcwU46/U4V+hxNr8Hl3JomwNBhXVv41KlWh0l9k4U6ZwotHOk2N6JEnsn8nVOXLR3Ic+pFTk6Zy46uJJj78pFR1cK7J1RazQYFYXKShOpeSVo1FUnSKP+3xk1KWhtNdjbqtHZ2rBi/3mc7WxrbN9BqyHU05FQTwfCPJ1k6KcQQoibzuTJk1m+fDlPPvkkCxYssFj27LPP8u9//5tJkyaxbNmyerW3du1ali1bxpYtW2jdujWenp61ltVl4MCBREZG8v777zd4ez/++CO2tn9c9wcOHHjVidoPP/zAc889x+LFi4mOjmbu3Lk89dRTnD9/vsFtAWzbto3Zs2dz8OBB0tPTWblyJWPGjLniOjNnzuSNN96wKIuIiCA+Pt6iLC0tjb/+9a/ExsZSWlpK27ZtWbp0KVFRUQ2q0xDz589n9uzZZGRkEBkZySeffELv3r2veZ266nz66ad8+umnpKSkANCpUydmzJhBTEzMVR1HU5LErJ7eeGsf65OKOHexFKPJhEatJtjdgX5tPWvc17X7dC55JXq8gGcdtdzS2oOEjEI2n8rAzcGWW1q7UVheQZinPRmFZew9k0dq+1CLIXj/V3Ce0spSUvOLOJNdiJ2twvm8YkyKgQhfBwyKgWNpeSQ/GMBKr3D6tPYg0FXH0fgUlC1LKCorxcHWSLCbDSh6HO0UtBoDFYYKyivLKCgrJfGO+8gxuZCQmoenTkOK5gQZeb9gr1FhMhpRKSYcbdTYqhQwmapeRiMORjt4egDo9VWv8nKyXI6S7pBDlqJUJY1GIxiMYDSgGI2ojFXjOG87C6/ssjy3/7yt6l+3MnArt/zX/X8vh4pyHCrK8SrIqfffzKRSU+LkSomrG7n2LhS08qTQzZu8Vl5kOLlzxtaFs/atKGjlhVGlo7C8guyiMgwmMCkKJpOCRq1CpVKhUavYfzYXF50WUKgwmnC11+LpaGfR+9bW25mRXf0kYRNCCHFDCgoK4ptvvuGjjz7C3t4egPLycr766iuCg4Mb1Nbp06fx8/Pj1ltvvWJZY6mtbXf3Woc2XZUPP/yQl156iQceeACAO+64o95Jam1KSkqIjIzkkUceYezYsfVer1OnTmzcuNH83sbG8ut+Xl4effv2ZdCgQcTGxuLl5UViYiJubm4NqnOpgQMHMnnyZCZPnlxj2YoVK5g2bRoLFiwgOjqaOXPmMHz4cBISEvD29q61vfqsU586gYGBvPvuu4SHh6MoCsuXL+euu+7i8OHDdOrUqd7n1RpUiqIodVe7eRUWFuLq6kpeXh7FivaqJ8u4Hu51qjBWUFJRQrmhnHJDOaWVpZRWllJmKKv6t7LqX61Gy7hO4yzWnb9vPnvS9lCkL8KoGGs2/r/ewFEBg3gy5B4oLoaSEpTiYu45PoNKg74qkTMYwFAJldUvA6rKSjxKTDwTp6VXUimUlABVvX4ZTuBVAo6VNTfZEOUurShy9ybLxYMsN1/OuniT4uxFoV8glUFhZNg6kldaQaG+kjJ91f1xatUfSZtGo0IxKmhs1Pi76vB01JnbdtBqiAxqVWfCZjKZyMrKwtvbG7VaJkwVTUdiTViLxFpN5eXlJCcnExYWhk6nq3uFFmTy5Mnk5+dz+vRpXnvtNR588EEAvvrqK/71r38RFhZGq1atWLZsGXq9nldeeYVvvvmGwsJCoqKi+Oijj+jVq5e5reXLl5vbDgkJYeDAgTXKUlJSWLt2Lf/85z85duwYGo2GPn368PHHH9OmTZsa7QAkJycTGhpaY99ra/vPPWT1bas2RUVFtGrVil27dhEdHQ3Ayy+/zMGDB9m8eXPdJ7cOKpWq3j1mq1atIi4u7rJ1XnvtNXbu3Mn27duvqc6lrpSYRUdH06tXL+bNmwdUfTYEBQUxdepUXnvttVrbq886V9MuVCXks2fP5tFHH611+ZX+P83Pz8fNzY2CggJcXFyufFIaSHrMGiDQzeGqk6prWddatBotWnvtVa37bO9neZZnURSFMkMZxRXFFOoLzf8W6Ysoqigi3D0c/NuY1yutKKEy1+uKbStADqB995/gG1mVsBUUkHBmF38/8B7oK3AyqPDTa/ErUeNfaMI/twK/jBL80wpxvpCDqrTsitvQFeajK8zHC6jttxOTkxNFPgFke/pz3tWbNM9AMnyCSfcL5ZyDG6VGhcKySvJKKzidVcwZVYl5XY1axcFzF/n2wDm8nHXobDT1TtaEEELcBKKiICPD+tv19YUDBxq82iOPPMLSpUvNidmSJUuYMmUKW7ZsMdd59dVX+eGHH1i+fDkhISG89957DB8+nKSkJNzd3c2J1aJFi9i/fz8ajQatVlujDKp6jqZNm0bXrl0pLi5mxowZ3H333cTFxfHxxx9z6tQp8/A0GxubWntgattebXVOnTpF586defPNNwHw8vJi2bJlTJkyhSv1ZRw5cgS1Wk1kZCSlpaV89dVXzJ07l5UrV5rrvPPOO7zzzjtXPLcnTpxocM/jpRITE/H390en09GnTx9mzZpl0eZPP/3E8OHDGTduHFu3biUgIIBnnnmGxx9/vEF16quiooKDBw8yffp0c5larWbIkCHs3r37qte5mnaNRiPfffcdJSUl9OnTp8HH0tQkMRONSqVS4WDrgIOtA96OtXdN/5mj1pGV962kUF9IXlkeeeV5Fv/mluWSXZJNdmk2Xo7/S+BsbcHTk+xCB/hfl3oxkPi/16Vc7Vz5YtgCVBkZkJYGaWmUpqWgu5CFOu0CXLhQVX7hAlRU1Lqf6uJiXIsTcD2dQNtLlpns7SkJaU1RaBuOO/lyxi2QdL8Q0n1DqbDTUaSvJDmnhHO5paTmlaJRq9GoVRxJzWP9iQxs1Wo0GhUTegXTw0d+URZCiJtO9fXpOvHQQw8xffp0zp6tmn1s586dfPPNN+bErKSkhE8//ZRly5aZ7+NZvHgxGzZs4LPPPuOVV17B1dUVZ2dnNBoNvr6+5rZrK7vnnnsstr9kyRK8vLw4ceIEnTt3RqvV4uDggK+vLzY2NqhUqhr7fLntXVrnz239uTwiIuKK5yQuLo727dtz8OBB+vXrB8DYsWMt7mN66qmnGD9+/BXb8ff3v+LyukRHR7Ns2TIiIiJIT0/njTfeoH///hw7dgxn56pZ4c6cOcOnn37KtGnT+Nvf/sb+/ft5/vnn0Wq1TJo0qd51Lk00y8rK2LNnD88995y57MSJE9jY2GA0GvHx8bHYVx8fnxr3vlXLycmpc5361Kl29OhR+vTpQ3l5OU5OTqxcuZKOHTvW+7xaiyRmotnZqG1wt3fH3b5h47x9HH0YHDaY7JJsMoozyC7NRqHmr1lOWidUTk7Qtm3VC5i/czZ70s4T6BxISKtbCHYNJsg5kDCjE14ZxajOnoXkZMvX2bNVvXWXUJeV4Rx/HOf441h8nKpUEB5OaYfOHHQNZKeDH2lB7Sj2CaC4wkh6QRmJmYWUV5pABSk5xQS52qKzO4uD1kZ61IQQ4mZxmUShpW7Xy8vLfP+UoijccccdFpN0nD59msrKSvr27Wsus7W1pXfv3pw8ebLB20tMTGTGjBns3buXnJwcTKaq+9bPnTtH586dr+oYGuLuu+/m7rvvvmKduLg4evToQZcuXdi7dy87d+7k73//O2+++SYzZ84EqobPNeY9bbX5cyLYtWtXoqOjCQkJ4dtvvzUP2zOZTERFRZmTqu7du3Ps2DEWLFhgTrrqU+fSRPPBBx/knnvusbgfzt/fn6ysrCY95vqIiIggLi6OgoICvv/+eyZNmsTWrVtbXHImiZm4bnXx6UIXny7m95XGSjKKM0gvTie9KJ0LRRe4UHThj562PzlXcI4KYwVn8s9wJv+MxTJnrTOtvVrTpl0bbgm8iw5eHaoWmExVvWpnzsCpU5CQUPWKj68qM15yb52iwKlTOJw6RX+gf3W5iwv6Dp1I8mvNIa/W/O7bjn323hTojfx+QQ+qUnOP2s+/X8DORk10mAcPRAdLkiaEEDeiqxhO2NweeeQRc8/I/Pnzm3Rbo0ePJiQkhMWLF+Pv74/JZKJz585UXGaUS3OIi4tj4sSJuLi40Lt3b3r37k1CQgJ79+4117HWUMY/a9WqFe3atSMpKclc5ufnVyMh6dChAz/88EOD6lyaaNrb2+Pt7U3btpZjizw9PdFoNGRmZlqUZ2ZmXrb3sj7rNKRdrVZr3q+ePXuyf/9+Pv74YxYuXFjr9puLJGbihmGrsSXINYgg16A66wa7BlNpquRC0YUavWxFFUUcyTzCkcwjtNK1+iMxU6sx+Puy03CaiB6j8HF89I/hEhUVVclZfHxVsnbyJBw7VvXS6y03XliI3d7ddGK3+X42o4MjZ4PbcTIgnPNtOnPcP4LDijunswoxGCE5t4S9ybnmqfzlHjUhhBDNacSIEVRUVKBSqRg+fLjFsjZt2qDVatm5cychISEAVFZWsn//fl544YUGbSc3N5eEhAQWL15M//5VP3Hu2LHDoo5Wq8V46Y+jV+lq2jIYDBw/fpwOHTpYlB85coRRo0aZ31tjKOOliouLOX36NBMnTjSX9e3bl4SEBIt6p06dMv+t6lunvrRaLT179mTTpk3myUtMJhObNm2yGPbY0HWupt1qJpMJ/aXfz1oASczETemVvq8AVTNRphWmcb7wPGfzz3I67zSn806TX54PQGu31hbrJecl8/7uquekuNq50t6zPREeEUR4RtCubTt07dtbbshggKQk+P33qteRI1X/njtnUU1TWkLr+MO0jj8Mm74FoNzZlVOhHdkf2JEDAR05WNaaEo0dUDVKcndyLtsSs3lhSDuLRy0IIYQQTU2j0ZiHJV46kYajoyNPP/00r7zyCu7u7gQHB/Pee+9RWlp62VnwLsfNzQ0PDw8WLVqEn58f586dqzHbXmhoKPv27SMlJYVWrVrh4eFx1bOAhoaGsnfvXlJSUnBycsLd3Z3Vq1czffr0y94PFR8fT3l5OW+++SZeXl44ODiYn5v15+Nt6FDG4uJii56u5ORk4uLizOcUYN68eaxcuZJNmzYBVTNBVvcwXrhwgddffx2NRmOewh/gxRdf5NZbb+Wdd95h/Pjx7Nu3j0WLFrFo0aIG1SkuLqa4uNj8/ptvvgEg408T2Xh5eaHRaJg2bRqTJk0iKiqK3r17M2fOHEpKSpgyZYq57qXHUp916lNn+vTpxMTEEBwcTFFREV999RVbtmxh3bp19f5bWIskZuKmptVoCXMLI8wtDP70I9DFsoucvniadh7tLOon5P7x61GBvoC9aXvZm1Y1TEGFitBWoXTw7EBn7870De6L2sYG2revev35V7L8fDh8GPbv/+P1v5uoq+mKCuh6dDddj+7mUcCgsSElpD2J4ZHs9mvPZs+2HDMpzFh9FB/nqmfJeDnbMb5XkCRqQgghmtyVpgp/9913MZlMTJw4kaKiIqKioli3bt0Vn4NVG7VazTfffMPzzz9P586diYiIYO7cuQwcONBc5+WXX2bSpElERkZSVlZW7ynua1PdVseOHc1tFRQU1Og9+rO4uDj8/Pywt7enf//+ODo60q9fPzZv3nzZoXr1ceDAAQYNGmR+P23aNACLh3jn5ORw+vRpc53U1FQeeOABcnNz8fLyol+/fuzZswcvrz9u6+jVqxcrV65k+vTpvPnmm4SFhTFnzhzzLJv1rfP+++/XeJj1par/Fvfddx/Z2dnMmDGDjIwMunXrxtq1ay0m7rj0WOqzTn3qZGVl8fDDD5Oeno6rqytdu3Zl3bp1DB06tM6/gbXJc8zq8OfnmLVq1aq5d0c0s+S8ZPam7SU+J56E3ASKK4prredu786yu5ZZzAxVbihHZ3P5Z9aYMjLI37SJVomJqA8cgH37IDv7ivtzzjuYPaGR7Aruwr7QSMpdWuHuYIu91oZgdwem9A2TJE3UIM+WEtYisVbT9fwcs5ZMURQMBsNlZ2VsSi+//DKnT5+2mBpfXN/kOWZCXAfMvWtUXQQuFF0wJ2kJOQkk5yejoNDZq3ONC8M/fvsHeeV5dPbuTKRPJN18u+Fm/6dfDr29qRg8GB54ANTqqslDkpJgxw7YubPq30t+sQvOOkdw1jnG7/sZk0rF6YBwdgR1YXtQV/a37kxyTjE+zvbSkyaEEEI0kbi4OIsZKIW4WpKYCXGVVCoVAS4BBLgEMLj1YADKKss4mXMSR1tHi7rlhnISLyZiVIxkJmeyKblq/HSoayjd/brTzbcbHTw6XLoBCA+velWPlc7OrkrSdu6E7dvh4MGq+9gAtaIQnnqK8NRTTNn9Awa1hqOB7dkZ1p097XvzempnvF0dJUkTQgghGtGRI0d4+umnm3s3xA1AhjLWQYYyisaQWZzJnD1zSMhNoNJU81loADYqG0IcQnix/4uEuNVz1qOioqoE7bffYNMmiIu7bNWLjq7sCOvBjvAokrr1xa91oMzseJOS4WXCWiTWapKhjE2jOYcyihtPcw1llMSsDpKYicZUYawgISeBuIw4DmccJuliknm6fkVRqNBX8M193+Du8EdvVn55PlqNFgfbeiRPOTmwZUtVkrZpEyQm1lrNhIpjAe3Y3z6axJ79KO7Uja4h7pKk3STky7KwFom1miQxaxqSmInGJPeYCXET0Gq05gdjT4ycSJG+6plph9MPczjjMGo7Na10rSzW+fb4t8QmxdLZqzO9AnrRy78Xfs5+tW/A0xPuvbfqBVXT8q9dC7GxsHEj/G9aWzUKXdMS6JqWAJs+J8fRjW3tb+GzqIHo+w9kbN+2MtRRCCGEEMKKpMesDtJjJqzFaDSSciGFsIAw8y/LiqLw+M+Pk1li+VT7AOcAegf0Jso/io5eHbFR1+M3loqKqnvT1qypStSOH6+1WqlWx6EOvTnR63bSbr2d0YM6SZJ2g5FeDGEtEms1SY9Z05AeM9GYZChjCyWJmbCW2r7AVBgrWHp4KfvS9pFVmlXrek5aJ3r79+au9nfVeCD2FVX3pv36K8b1G9CUl9WoYlCr+b11JMeiBhI05QEGDet1VccmWhb5siysRWKtJknMmoYkZqIxSWLWQkliJqzlSl9gFEXhfOF59qXt48CFA5zIPmG+N63amwPfpLtf96vbeGkpbNgAq1dTuWo1tnkXa62W0roTKYNGUnLXGCL7dZP70a5T8mVZWIvEWk2SmDUNScxEY5J7zJpYaWkpHTp0YNy4cbz//vvNvTtCNIhKpSLYNZhg12Du7XgvRfoiDqUfYl/aPvZf2I9apaaLTxeLdTYnb2br2a3cEngLtwTeUuPeNQsODnDXXXDXXdguMsCuXbB6NeXf/4juXIq5WuiZ44SeOQ6fzSYxtAM/3jKM8rvu5rbhvSRJE0IIIYS4BjdNYvb2229zyy23NPduCNEonO2cGRA6gAGhA6g0VpJamFrjPrPt57ZzMP0gB9MP8u/9/6ajV0f6Bfejb1BfywdbX8rGBm67DW67Dd3778Px46Qt/QrVDz/gf/aUuVp4yknCU07CNx9zOrQD5x+4n6AnHobQ0CY6aiGEEEKIG9dNMa4gMTGR+Ph4YmJimntXhGh0thpbwtzCLMpMiom0wjTzewWF49nHWXhwIZNWTeL/Nv0fa5PWUqgvvHLjKhV07kzAB+/gn5JAxr44jj79ClmtIyyqtUk5SdCs1yEsjHPhXTg34x3IyGi0YxRCCCGEuNG1+MRs27ZtjB49Gn9/f1QqFatWrapRZ/78+YSGhqLT6YiOjmbfvn0Wy19++WVmzZplpT0WovmpVWoWjFrAh8M+ZFzHcQQ4B5iXKSj8nvU78/fPZ+LKiWw7u63e7fr2iqTLv9/D+3Q8JCSQ+vL/cSGknUWd4KRjBL/1fxj9A0jp0ZeL/14EhXUkgEIIIYQQN7kWP5SxpKSEyMhIHnnkEcaOHVtj+YoVK5g2bRoLFiwgOjqaOXPmMHz4cBISEvD29mb16tW0a9eOdu3asWvXrjq3p9fr0ev15veF//tCaTKZMJlMjXdgQlzCZDKhKEqjxlkbtza0cWvDg50f5GzBWbaf286OcztIL04HwKgYaevW1mKbRfoiNGpN3Q+0btsW/3+9Cf96k983HyDtP1/Qaec6gs9XPdRao5gIPbwLnt1F5QvPUzR0BK0emwQxMaDVNtoxioZrilgTojYSazVVn5Pql2g81edTzqu4VtX/f9b2/b8pP8+uq1kZVSoVK1euZMyYMeay6OhoevXqxbx584CqkxUUFMTUqVN57bXXmD59Ol9++SUajYbi4mIqKyt56aWXmDFjRq3bmDlzJm+88UaN8vj4eFxdXZvkuISAqtgtKCjA1dW1SWcvUxSFlMIU9mXsI7M0k+e7P2+x/LtT3xGbHEs372709e9LV8+u2Gps691+0o7D5C39hp571uN/seZwxjInF0ruuAPVfeOojI4GmanN6qwVa0JIrNVUWVlJQUEBISEhN9ysjEOGDCEyMpIPPvjA6ttWFAWj0YhGo2nQrIyNvc/1bS83N5euXbuyc+dOQv90b/bnn3/O+++/z9mzZwkODuZf//oXI0eObJR9aywPPvggUVFRvPjii829K02mvLycs2fP4urqiq2t5XeggoIC2rdvL9PlX5qYVVRU4ODgwPfff2+RrE2aNIn8/HxWr15tsf6yZcs4duzYFWdlrK3HLCgoiNzcXJkuXzQpk8lEdnY2Xl5ezfYFRlEUnvr1KXOPGlQ9J61fUD8GhAygo1fHel/w0i6WcuCbX3Fb/QPdd6/HtaSgRh29XwDayQ+jPPwwtGtXSyuiKbSEWBM3B4m1msrLy0lJSbnupsuv6+83Y8YMtm7dSmRkJHPmzLHOTl2isrKyxpfoPxs0aFCN/bt48SK2trY4Ozs3yj7Uto3aTJs2jaKiIhYvXmwu++GHH5g8eTKLFi0iOjqauXPn8uOPP3Lu3Lmr2pdt27bx/vvvc/DgQdLT0/nxxx8tvi/XZubMmbz55psWZREREZw8edL8/tixYwwYMIAzZ87csJ0W1dPlV98q9Wf5+fl4eHjIdPmXysnJwWg04uPjY1Hu4+NDfHz8VbVpZ2eHnZ1djXK1Wi0XFdHkVCpVs8ZahbGCKP8otp/bToG+KpEqqSxh3Zl1rDuzDm8HbwaGDmRg6ECCXIOu2FaQpxNBz90Hz93HwcRMjiz5jrabfqZX3FbsK6t+/LBLT4NZs1DNmgV9+sDkyTB+PMiPIE2uuWNN3Dwk1iyp1WpUKpX5db1IT//jB7sVK1YwY8YMEhISzGVOTk5s3bq1WY6roqICW1tb83avtP1L98/Dw6PR96euc1BaWsqSJUtYt26dRb2PPvqIl156iQkTJgAwatQoli9fftXns7S01OJ2oPr8bVQqFZ06dWLjxo3mskufDdelSxfatGnDf//7X5599tmr2reWrvpc1fbZ1ZSfZTfVp+TkyZPlGWZCXIFWo+XJqCdZPmY5bwx8g0Ghg7DT/PFDRVZpFt+e+JZn1jzDgQsH6t1uz3AfHpn1HK3XrWTht7uYM2UGe9tHY/jzh9vu3fDkk5h8/eCBB2DdOjAaG/PwhBBCXCVfX1/zy9XVFZVKZVHm5OQEVPWSvvrqq7i7u+Pr68vMmTMt2jGZTMyaNYuwsDDs7e2JjIzk+++/Ny/X6/U8//zzeHt7o9Pp6NevH/v377doY+DAgTz33HO88MILeHp6Mnz4cEwmE//6179o3bp1re1OnjyZrVu38vHHH5u/dKekpDBw4EBeeOEFi/177733aNu2LXZ2dgQHB/P222+bl69du5Z+/frRqlUrPDw8GDVqFKdPn27QuVyzZg12dnYWj3EqKipiz549FsMW161bR/fu3RvU9p/FxMTwz3/+k7vvvrtB69nY2Fj8bT09PWvUGT16NN98881V75uo3XXdY+bp6YlGoyEzM9OiPDMzE19f32baKyGufxq1hh5+Pejh14Nnej3DntQ9bEnZwqH0Qygo2NvY08Xb8oHWOaU5ONo6Ym9rf9l2A90ceGFMDxjTgwMpf+GdDXH4/foDA/fEEp6ZDIBaXw7ffAPffIPRzw/Nww/DpEnQoUOTHrMQQjSnVfGrWBW/qs56bdza8I8B/7Aoe2vrW5zOqzs5GNN+DGPaj7nKPayf5cuXM23aNPbu3cvu3buZPHkyffv2ZejQoQDMmjWLL7/8kgULFhAeHs62bdt46KGH8PLyYsCAAbz66qv88MMPLF++nJCQEN577z2GDx9OUlIS7u7uFtt5+umn2blzp0W7n376Ke3atavR7scff8ypU6fo3Lmzeaiel5dXjf2fPn06ixcv5qOPPqJfv36kp6dbjMIqKSlh2rRpdO3aleLiYmbMmMHdd99NXFxcvXtStm/fTs+ePS3Kjhw5glqtJjIyktLSUr766ivmzp3LypUrzXXeeecd3nnnnSu2feLECYKDg+u1H5eTmJiIv78/Op2OPn36MGvWrBpt9u7dm7fffhu9Xl/rSDNxda7rxEyr1dKzZ082bdpkHjNrMpnYtGkTzz33XPPunBA3CJ2Nzjx8Mb88n+1nt1NmKMPOxvKD+LNDn7H/wn76BvVlcOvBdPHucsUhE1Gh7kQ9fjsHhnZj8b7HsT9+lM4bVzLk8CbcyqpmQ9Wkp8O//lX1io6uStDuvx/crvCAbCGEuA6VVpaSW5ZbZz1Ph5q9FwX6gnqtW1pZelX71hBdu3bl9ddfByA8PJx58+axadMmhg4dil6v55133mHjxo306dMHgNatW7Njxw4WLlxIVFQUn376KcuWLTM/e3bx4sVs2LCBzz77jFdeecW8nfDwcN577z2gqpdt1qxZ5t4slUpl0e6AAQNwdXVFq9Xi4OBw2R/vi4qK+Pjjj5k3bx6TJk0CoE2bNvTr189c55577rFYZ8mSJXh5eXHixAk6d+5cr3N09uxZ/P39Lcri4uJo3749Bw8eNG9v7NixFs/gfeqppxg/fvwV27603YaKjo5m2bJlREREkJ6ezhtvvEH//v05duyYxX14/v7+VFRUkJGRQUhIyDVtU/yhxSdmxcXFJCUlmd8nJycTFxeHu7s7wcHBTJs2jUmTJhEVFUXv3r2ZM2cOJSUlTJkypRn3WogbUytdK0ZHjK5RXlJRwr4L+6gwVvBbym/8lvIb3g7e3B52O7eH3Y6fs99l24wKdScq1B3oRuy9Q3j8t5NEHNzBsANr6ZuwDxvT/4Yz7t0Le/eivPgiqrFj4bHHYOBAmdVRCHFDcLB1wMO+7vudXO1qTrbgaudar3XrfAxKI+jatavFez8/P7KysgBISkqitLTU3HtWraKigu7du3P69GkqKyvp27eveZmtrS29e/e2mHwCsOhxqm73z0nMn9utr5MnT6LX6xk8ePBl6yQmJjJjxgz27t1LTk6Oeer0c+fO1TsxKysrqzGhRFxcHD169KBLly7s3buXnTt38ve//50333zTPBzU3d3dotewKfz5HHbt2pXo6GhCQkL49ttvefTRR83L7O2rRseUljZ9sn8zafGJ2YEDBxg0aJD5/bRp04CqmReXLVvGfffdR3Z2NjNmzCAjI4Nu3bqxdu3aGhOCCCGaToWxgsFhg9l2dhsllSVA1f1o3xz/hm+Of0Nnr84Mbj2YvkF9rzjUMaaLH10CXdndN5x9OeNYceIMEZvXMGz/WjpkngFApdfD11/D119jCA3D5vHHqiYNucZfCYUQojldyzDDS4c2NqdLZ0VUqVTm5KW4uBiAX3/9lYCAAIt6dnZ25OXl1Xs7jo6O5v+ubnf16tUEBwdbjNZoyDC76mTjSkaPHk1ISAiLFy/G398fk8lE586dqaioqPd2PD09axxrXFwcEydOxMXFhd69e9O7d28SEhLYu3evuY61hjL+WatWrWjXrp1FJwlUzWYJtQ8HFVevxSdmAwcOrPNBgc8995wMXRSiGbnZu/FMr2d4rMdj7Evbx8YzG833owEcyz7GsexjLDiwgH/f8W+8Hb0v21agmwPjoqp+1U2NDmFNz/a8d/phbI8f5fY9sYyI20ir0qqhjjYpyfB//wczZsDIkVW9aCNHgk2L/2gTQoibTseOHbGzs+PcuXMMGDCgxnJ3d3e0Wi07d+40D4+rrKxk//79FhN0XKnd22+//bLD6LVaLcYrTCoVHh6Ovb09mzZt4rHHHquxPDc3l4SEBBYvXkz//v0B2LFjx5UOuVbdu3fnyy+/NL83GAwcP36cDpfcS33kyBFGjRplfm+NoYyXKi4u5vTp00ycONGi/NixYwQGBtY6MYi4evLtRQjRaLQaLf2C+9EvuB8Xyy6yOXkzm5I3cb7wPAC+Tr54OVj+uqY36Gvcr1Yt0M2BJwa04YkBbUjN68Ka3wfxwolU2uz6jaG7f+GW04eqKhqN8PPPVS8/v6oetEcegbZtm/JwhRBCNICzszMvv/wyL774IiaTiX79+lFQUMDOnTtxcXFh0qRJPP3007zyyivmW1bee+89SktLLYbR1dbuSy+9xCuvvIJKpaJ///412gUIDQ1l7969pKSk4OTkVGNYoE6n469//SuvvvoqWq2Wvn37kp2dzfHjx3n00Udxc3PDw8ODRYsW4efnx7lz53jttdcafB6GDx/O9OnTycvLw83Njfj4eMrLy3nzzTfx8vLCwcGBTz/9lJSUFIvjbuhQxrpuB5o3bx4rV65k06ZN5jovv/yyuVfwwoULvP7662g0Gh544AGLtrdv386wYcMafOziyiQxE0I0CXd7d+7peA9jO4wl6WISG89sJMwtrMYvmX/d+Fd0NjoGhw2mf0h/dDa1P3C1Okkb2dWP3b1as/3B+1my53e6/7aau+PW41v0vxvf09Nh1qyq16BBVb1oY8fCdfQgVyGEuFG99dZbeHl5MWvWLM6cOUOrVq3o0aMHf/vb3wB49913MZlMTJw4kaKiIqKioli3bh1udUz69NZbb+Hh4cG7777LE088UaNdqEo6Jk2aRMeOHSkrKyM5OblGO//4xz+wsbFhxowZXLhwAT8/P5566img6vlV33zzDc8//zydO3cmIiKCuXPnMnDgwAadgy5dutCjRw++/fZbnnzySeLi4vDz88Pe3p7+/fvj6OhIv3792Lx58zXNMl7X7UA5OTk1pvpPTU3lgQceIDc3Fy8vL/r168eePXsshiyWl5ezatUq1q5de9X7JmqnUuoaJ3iTKywsxNXVlby8PFrJQ29FEzKZTGRlZeHt7X3TPIg1OS+Z59c+b36vs9HRP7g/w9sMp51HuzofhHkg5SJLdySTmltE56N7GLL7F/rH7/ljwpBqbm7w4IPw+ONwyY3pN6ObMdZE85BYq6m8vJzk5GTCwsJqTAAhrp6iKBgMhhoPQ26pfv31V1555RWOHTvGq6++yunTpy2mxm/JPv30U1auXMn69eube1eazJX+P83Pz8fNzY2CggJcXFwadbvSYyaEaDZFFUUEuQSZhzqWG8rZcGYDG85sIMgliGFthjEodBCuupqzkMGfZ3SEAyldWbh1MB+dSmHQvljuPrSO0IsXqirm5cG8eVWvW26Bp56C8eOhHjd6CyGEEI3tjjvuIDExkbS0NOLi4ixmomzpbG1t+eSTT5p7N25I0mNWB+kxE9Zys/6yrCgKp3JPsfHMRrae3UqZocxiuY3ahr5BfXmpz0t1/gqamlfKmt/TOXI+j1K9Ecd9uxi6+xeGn9yBznDJjFmtWsHDD8OTT0LHjo18VC3bzRprwvok1mqSHrOmcb31mP2Zl5cXCxYsqPGMNNF8pMdMCHFTUqlURHhGEOEZwaM9HmXnuZ2sP72eEzknADCYDFQaK+t1oa2+D61abO9gFnaNYl5GLoMOrueeg7FEZKVULczPh7lzq179+1f1ot1zDzRgamUhhBDiWmVnZzf3LogWQhIzIUSLobPRMbj1YAa3HkxqYSobTm9gU/ImhraxfBhppbGS93e9T7/gftwSeAu2Gtta26t+Ltqa39M5EhHIu/dMwu3oQQZtXcnQY9v+6EXbvh22b8c49Xk0j0yBJ56A8PCmPlwhhBBCCDMZylgHGcoorEWG/NTOYDKgVqlRq/44JzvO7eBfO/8FgLPWmUGhgxjaZiihrULrbO9AykW+3X+exPiz9NkVy7gDvxKWc75mxdtvr+pFu+su0Gob63BaBIk1YS0SazXJUMamcT0PZRQtjwxlFEKIWtioa35MHbhwwPzfRRVF/HTqJ3469RPt3NsxtM1Qbgu5DQdbh1rbq54w5EBKEAtDfHns9nG0TzrC6D0/c/vxHWiNlVUVf/ut6uXtDY8+WjWjY1hYkxyjEEIIIYT0mNVBesyEtcgvy/WnKApHs46y/vR6dp3fRaWp0mK5ncaO20JuY2T4SNq6X/4h06l5pew+nUteiZ6Cskp+j0ui55afuHv/GkKqZ3Ss3qZKhWr48KrJQkaNApvr93ctiTVhLRJrNVX/Eh8aGoq9zAzbaKTHTDSmsrIyUlJSpMdMCCHqolKp6OrTla4+XSmuKGZrylbWn17PmfwzAOiNejac2YCLncsVE7NANwfGRf3Rs3agvQ//dG7F8uixRCXHMf5QLINO7sLGZESlKLB2Laxdi9HPD82TT1bdi+bn1+THK4S4cWg0GgAqKiokMROihSotLQWqHg1gTdJjVgfpMRPWIr8sX7vTF0+z/vR6tpzdQmllKQtHLcTf2d+8vKC8gPTidCI8Ii77i+qBlIusOZpOpdFEck4x+nMXGLjnV8bsX0NAfqZlZRsbuPtueOYZGDAArpNfaSXWhLVIrNWkKArnzp2jsrISf39/OS+NRHrMRGNQFIXS0lKysrJo1aoVfrX8+NqUPWaSmNVBEjNhLfIFpvGUG8o5mnmUXgG9LMq/Pf4tX/z+BSGuIQxvM5xBYYNw0jpdtp3qoY4pOcX8fu4inru2cueeX7jt1F40ismibmVEB2ynPgsTJ0Ijf1A3Nok1YS0Sa7WrqKggOTkZk8lUd2VRL4qiYDKZUKvVkpiJa9aqVSt8fX1rjSVJzJqRJGbCWuQLTNNSFIXHfnqMrNIsc5lWo6VfUD9GtB1Be8/2V7yYVz+8es3RC+hTzjJm7y/ce3gdHiX5lhUdHauSs2eegS5dmuhoro3EmrAWibXLM5lMVFRU1F1R1IvJZCI3NxcPDw+JNXFNbG1tzUOOayOJWTOSxExYi3yBaVpGk5EtKVtYd3odJ3NO1lge5BLEiLYjGBQ6CGc758u2Uz3dfnaRnty8Irru38Q9e3+me8qxmpX7969K0MaObVFT7kusCWuRWBPWIrEmrEUSs2YkiZmwFrmoWM/Z/LOsO72O35J/o6SyxGKZrdqWmQNn0tWna53tVN+PlllYzsU9B7hz10/cdew3HCrKLSt6e1dNt//EExAc3JiHclUk1oS1SKwJa5FYE9YiiVkzksRMWItcVKyvwljBznM7WZu0lhM5JwDQ2ej44u4v0Nn8MT2uoih1DnP8eu85Nidkos/NZ/CBdYw/8Ctts89ZVlSr4c47q3rRBg+uet8MJNaEtUisCWuRWBPWIolZM5LETFiLXFSa1/mC86w7vQ5btS2Tuk2yWDZ/33zKDGWMaDuCTl6dLpukVd+HduR8HlmFenzj9jBq5ypuj9+NrcloWTk8HJ5+GiZPBje3Jjqq2kmsCWuRWBPWIrEmrEUSs2YkiZmwFrmotEwlFSU8vOphKoxVN+kHOAcwvM1wBrcejIvd5T+Qq5O0DScyKDxzjjv3r+HeQ7H4FOVa1DPZ26OeMKGqF61HjyY9FvM2JdaElUisCWuRWBPWIolZM5LETFiLXFRappPZJ3lr21sUVRRZlNuobbg18FZiwmPq3YumL62g/YHNDPztB6JOH65ZOTq6KkEbPx50uprLG4nEmrAWiTVhLRJrwlokMWtGkpgJa5GLSstVYaxgT+oe1iat5WjW0RrLq2d0HBk+Ehu1zRXb+u7AeX48lIpLciKDt/5IzKENOOtLLSt5eFRNFvLUUxAS0piHAkisCeuRWBPWIrEmrEUSs2YkiZmwFrmoXB/SCtNYd3odG89stOhF83fyZ8GoBXU+2DQ1r5TEzGKcdTZ8u/88h0+eZ/iRTdy792dC005bVq6eLGTqVBg0CBrpoakSa8JaJNaEtUisCWtpysTsyj/tCiGEsBDgEsAj3R/hoa4Psfv8bmKTYjmefZwRbUfUSMp2nd9Fd9/u2Nvam8sC3RwIdHMAwNdVx+4wd9aHeDOu2wjanTnGQwd/YciJHdgaDWAywapVVa8OHeC556oeXu18+eesCSGEEOL6JD1mdZAeM2Et8mvf9et8wXnc7N1w0jqZy84VnOPZNc+is9ExMGQgMeExtHZrXev6f35odWZROZVpFxi971fuO7gGn+KLFnVNTs6op0yGZ5+FiIir2l+JNWEtEmvCWiTWhLXIUMZmJImZsBa5qNxYFh1cxM+nfrYoi/CIYETbEfQP7o+djV2t61UnaSfTCykpKaPfse3cvWs13VNq3tvG0KFVwxxHjgSNpt77JrEmrEViTViLxJqwFknMmpEkZsJa5KJyY0nOS2ZN4hq2nN1CuaHcYpmjrSO3h91OTNsYglyDal2/+l608kojPx5KRXXkCDHbf2RE3G/YG/SWlUNDq2ZzfOSRqolD6iCxJqxFYk1Yi8SasBZJzJqRJGbCWuSicmMqrSxla8pWYpNiSc5PrrF8bPuxTOk+5YptpOaVsvt0Lik5xRw/nkL3Tau5Z+9PBF5Mt6in6HSoJkyouhete/fLtiexJqxFYk1Yi8SasBaZ/EMIIa5TDrYOxITHMKLtCE7lniI2KZbt57abH1jd0atjnW0EujkwLqpqwpDU6BCWtAvmySHjaRe3k3t3/0TfpAMAqMrLYcmSqtett1YNcxw7FrTapjtAIYQQQjSKGz4xO3/+PBMnTiQrKwsbGxv+8Y9/MG7cuObeLSHETUalUhHhGUGEZwSP9XiM35J/Y3/afqL8oyzq7U/bz08JPxETHkPvgN41nosW6ObAI/3C6ODnQkpHPz69bQiLEpMYsWMlow6u++OZaLt2Vb18feHJJ+GJJ8Df31qHK4QQQogGuuGHMqanp5OZmUm3bt3IyMigZ8+enDp1CkdHx3qtL0MZhbXIMAwB8MaWNziQXtUD5qZzY1ibYQxvMxwvR69a6/95mOPu31OI3LaGCft+Jjz7rEU9xcaGrKF3oJr6HJ7DBpGVnS2xJpqcfK4Ja5FYE9Yi95g1osjISH755ReCgmq/4f5SkpgJa5GLiqgwVjB1zVQuFF+wKFehIso/ipi2MfT074laVXt8VM/oeCa7CL+4vdy5YyWDEnZjYzJZ1FO6daNw4kScn3gCtZNTrW0J0Rjkc01Yi8SasJamTMxafORu27aN0aNH4+/vj0qlYtWqVTXqzJ8/n9DQUHQ6HdHR0ezbt6/Wtg4ePIjRaKx3UiaEENak1WhZMGoBbw16i1sDbzUnYAoK+y/s581tb/LYT4+x4tgKCsoLaqwfFerOe+MimfNAD7o8OIZVf5vDI/9YwX9ue4BcB1dzPVVcHK4vvYQSFAyvvAJnzljtGIUQQghRuxZ/j1lJSQmRkZE88sgjjB07tsbyFStWMG3aNBYsWEB0dDRz5sxh+PDhJCQk4O3tba538eJFHn74YRYvXnzF7en1evT6P6aiLiwsBKp+iTFd8quzEI3JZDKhKIrEmaCrd1e6enflYtlFNpzZwLrT68gpzQEgqySLL37/guiAaJy1zrWu7++q47H+YUAYB1PC+LZjW57LeJyOO9YxZtdKuqSdAkCTnwfvv4/ywQcwciTKs89WPRtNfm0WjUQ+14S1SKwJa2nKGLuuhjKqVCpWrlzJmDFjzGXR0dH06tWLefPmAVUnKygoiKlTp/Laa68BVcnW0KFDefzxx5k4ceIVtzFz5kzeeOONGuXx8fG4urrWsoYQjcNkMlFQUICrq6sMwxAWTIqJ37N/57fzv3Ek+wjt3Nrxf9H/Z1HnTMEZPHWeuNjVPqwivVDPplN5nMwoxvXE7wze/CNDj25FazRY1DO0aUPp5MmUjR+P0shDNMTNRz7XhLVIrAlrKSgooH379nKP2aWJWUVFBQ4ODnz//fcWydqkSZPIz89n9erVKIrChAkTiIiIYObMmXVuo7Yes6CgIHJzc+UeM9GkTCYT2dnZeHl5yUVFXFZWSRbFFcW0dmttLlMUhWfWPENmSSa3Bt7KiLYj6OTVCZVKVWsb53NL+G5PElnnson49TtG7lyNX2G2RR2jgyPqhydW9aJ1rHtKfyFqI59rwlok1oS15Ofn4+HhIc8xu1ROTg5GoxEfHx+Lch8fH+Lj4wHYuXMnK1asoGvXrub707744gu6dOlSa5t2dnbY2dnVKFer1fI/umhyKpVKYk1cka+zb42y3zN/N08Ysv38draf306wSzAx4TEMCh2Eo9ZyFtogD0ce6uWH9x2R/KdzGx47cD/d4rZz967VRJ2JA0BTWgILFqBasIDy2wagm/YijBoFGk2TH6O4scjnmrAWiTVhDU0ZX9d1YlYf/fr1k/HGQogbmp+TH2Pbj2XDmQ0UVRQBcK7wHAsPLmT5keUMCBlATNsY2ri3qbHuyK5+hPs4Uz6sIwsP3cGSkycYvu1Hhh5cj0NFOQC6bVth21ZK/AOpfOIpWk19GtzdrXqMQgghxI3uuk7MPD090Wg0ZGZmWpRnZmbi61vzV2UhhLgReTl6MaX7FB7s+iC7zu9iTeIaTuacBKDcUM660+tYd3odXby78Pbtb1usG+jmQKCbAwBdAl1JjA6h/MFhvLYjnrBfv2PsrtWE5FX1xjleSIWZf8cw65+U3/cATi+/CJcZfSCEEEKIhrmuEzOtVkvPnj3ZtGmT+R4zk8nEpk2beO6555p354QQwsq0Gi0DQwcyMHQgKfkpxCbG8lvKb5Qbqnq+vB29UalUXO7W4kuTtDUdg5l9djL+e7cxZNN39E6oehSJjb4cp8+XwudLyepxC+q/PI/nhHFgc11fUoQQQohm1eKvosXFxSQlJZnfJycnExcXh7u7O8HBwUybNo1JkyYRFRVF7969mTNnDiUlJUyZMqUZ91oIIZpXaKtQnu71NJO7TWbr2a2sSVzDyPCRFnXKDeW8v/t9BocNJjowGhv1H5eEQDcHnhjQBmhD6ujO7J5yH1t2HqLdD18wZF8sTvpSALwP7YFJeyh+5SWMTz2F69RnwNPTmocqhBBC3BBa/KyMW7ZsYdCgQTXKJ02axLJlywCYN28es2fPJiMjg27dujF37lyio6MbZfuFhYW4urqSl5cnszKKJmUymcjKysLb21tuXBaNrvqjXqVSmWPtUOEhPj34KQBuOjeGtRnGiLYj8HSoPbFKzStl9+lc0s5lov3qC2K2/EhYbqpFHaOdHeX33ofjyy9Ct25Nekyi5ZPPNWEtEmvCWvLz83Fzc5Pp8puDJGbCWuSiIqylOtY+O/UZe9L2WCxToaJ3QG9i2sbQw6/HZafcP5BykTVH0gg+vIvIHz8n8thu1JdcTtK7RKF98S94PHQf2No22fGIlks+14S1SKwJa5HErBlJYiasRS4qwlqqY83Ly4uj2UeJTYxlT9oeTIrlDLY+jj6MaDuCoa2H4qpzvWx7qXmlrPxuKwFfLWXYnl/NwxyrVfj6oX3uWXjiCfDyapJjEi2TfK4Ja5FYE9YiiVkzksRMWItcVIS11BZruaW5bDizgbVJa8kty7Wo/1CXh7iv831XbLN6mOORk+fxXPUtd25fSevscxZ1DDa2HLstBu0Lf6Hj6Nsb96BEiySfa8JaJNaEtUhi1owkMRPWIhcVYS1XijWjycj+C/tZk7iGwxmH0ag0LL1rKW72buY6Rfoi1Cp1jQdXwx8JWl5xOa67txP69RJ6HdtVY5hjTpceqJ6fisfDE0CrbZoDFc1OPteEtUisCWuRxKwZSWImrEUuKsJa6htr6UXpxOfEMyjMcgKmpYeXsiZpDQNCBjAyfCSt3Vpfto0DKRfZ8OseOq36kkE7fsa5vNhiud7Lh/JHH8f1hefAx+faDky0OPK5JqxFYk1YiyRmzUgSM2EtclER1nItsVZhrGDyqskUVRSZyyI8IohpG0P/kP5oNbX3fqXmlbLveCqmL76k1y//JeTCGYvlRhtbUoeOQjftBXyG3NbwgxItknyuCWuRWBPW0pSJmUSuEEKIetMb9PQP7o/ORmcuS8hNYM7eOUxaNYn/HPoPaYVpNdYLdHNgbL923PLua6xctoa/Pf8xv3Xsh1FVdRnSGCoJiV2Jz9ABZHXsxsWFn4Feb7XjEkIIIZqb9JjVQXrMhLXIr33CWhoj1soqy9iSsoU1iWtIKUipsTzSJ5IXbnmh1meipeaVsub3dJKyirC7kEqXn75i+O5fcC0rsqhX6ubJyTvv58J9D9P9lk4Eujlc1b6K5iOfa8JaJNaEtchQxmYkiZmwFrmoCGtpzFhTFIWE3ATWJK5hx7kdVJoqAXC1c2XZmGXYqG2uuH71ZCGHE9Lwj13NHVt/ICw10aKOQa3hUK/bcX71JTrcPQwu82w10fLI55qwFok1YS2SmDUjScyEtchFRVhLU8Vakb6IjWc2EpsUS9+gvkzqNsli+Y8nfyS0VSjdfbvXeHB1al4piZnF5BSVkbRyHX1+/Yp+x7ZjY7J8tlpmeCdKn3yasGcfBZ0O0bLJ55qwFok1YS2SmDUjScyEtchFRVhLU8eaoihUmiotJgK5WHaRKaunYFJM+Dr6MqLtCIa0HlLjwdXm6fZL9DhmpdPxp69pu/prnIvyLeoVObuReNcD+P31Bfw6hzf6MYjGIZ9rwlok1oS1SGLWjCQxE9YiFxVhLc0Raz+c+IFlR5ZZlNmobegX1I+Y8Bg6eHao0YtWLTX9Ilve/IRev3xFROopi2VGtYaCEaNwf+0l6NdPhjm2MPK5JqxFYk1YiyRmzUgSM2EtclER1tIcsWY0GdmXto81iWuIy4yrsTzENYSR4SMZGDoQB9uak3wcSLnIjsRs2icfx3f5Yjrv2YCNyWhR53xIO87cNwWnKRMpxJZwHyeZMKSZyeeasBaJNWEtkpg1I0nMhLXIRUVYS3PHWnpROrFJsWw8s9HieWgAnb06M2vIrDrbuHDiNMdff48ea7/DozjPYlmhoyv7h4zF/vnnuPX2Ho2676JhmjvWxM1DYk1YizzHTAghxA3Dz9mPR7o/wrIxy5h2yzQ6eHYwL7s97HaLuoqiUGGsqNGGf8c2dFj0ESt/3MGyp97gdFgn8zKXkgIGr17KLUN6cTR6CAnf/ATyG6QQQogWTnrM6iA9ZsJa5Nc+YS0tMdZS8lNYf3o9D0c+bPHw6viceN7c+iaDwwYTEx6Dv7P/ZdvI3LiNwvc+JOy3X7ExGiyWFYZ34MJDj+L86CQCAmo+W000jZYYa+LGJLEmrEWGMjYjScyEtchFRVjL9RRrH+7+kM0pm83vI30iGRk+kt4BvS/7jLQL8Wc49vr79Fj7LZ6FuRbLyp1duXDPBLYMvpeu/boRFerepPt/s7ueYk1c3yTWhLU0ZWJ25Sd/CiGEEM1EURTsNHbYqm3ND64+knmEI5lHcLd3Z1jrYQxvOxxPB8seMP/2rTEteJ9j5/9Gq7U/Y7/oUyJOHwVAV1RA62WfErJ8Ifs63cqKCY+gHnI7fdp6yUQhQgghmpX0mNVBesyEtcivfcJarrdYK9QXsunMJmKTYkkvTrdYpkJF74DeTOgygdZurWtd/0DKRTZ/FUvUT/+l74GNaI2VFsvP+oVx7v7JmB6aSJswH0nQGtH1Fmvi+iWxJqxFhjI2I0nMhLXIRUVYy/Uaa4qiEJcRR2xSLHvT9mJSTOZlswbPorN358uuW/3g6qyks7RZ/Q19NnyHa26WRZ1inRO7B4zGd/pLdBnQs8mO42ZyvcaauP5IrAlrkcSsGUliJqxFLirCWm6EWMspzWH96fWsO70OR1tH5o+cb/GA6hPZJwAu/+Dqykpyv1yB6ZNP8Dq8z2KRSaXieGQ/4u+dRF7f23BzsqNPG0/pSbsKN0KsieuDxJqwFknMmpEkZsJa5KIirOVGijWDyUBOaQ6+Tr4W5a+sf4X43HhCXUOJCY+57IOrAY6v2UrFRx/TaesatJV6i2UpXsH8etvdFI2bwEPDOkty1kA3UqyJlk1iTViLJGbNSBIzYS1yURHWcqPHWnJeMs+vfd6iTGejY2DIQEaGjyTMLazW9S6cPs/59z4h/IfPcc/NtFhWonNk922jSL5vCq26dpAetHq60WNNtBwSa8JaJDFrRpKYCWuRi4qwlhs91iqMFew8t5PYpFhO5pyssTzCI4KR4SPpF9wPrUZbswGDgZyvvsM09xO8D+62WGRSqTjY8RbKnnya1hPuJjG7lHAfJ0nSLuNGjzXRckisCWuRxKwZSWImrEUuKsJabqZYS85LJjYpls0pmyk3lFssc7VzZfHoxdjb2l++gaNHufDWe3is+g67S4Y5pvuGsGXYeM6OvBd3X3fcHLXSk3aJmynWRPOSWBPW0pSJmUSuEEKIG1aYWxjP9HqGz8d8ztNRTxPqGmpe1s6j3ZWTMoAuXTAtXEhs7H72PPUqRT7+5kV+GWd54PPZTJ18O74z/8ahTfv5/mAqqXmlTXQ0QgghbmTSY1YH6TET1iK/9glruZljTVEU4nPiiU2KZWDoQHr49TAvM5gM/HXDX4nyj2JYm2F4OHjUbMBgYOdHS2n12QI6JRyqsfhw5z4cvPMhTEOGgFp90/ei3cyxJqxLYk1YiwxlbEaSmAlrkYuKsBaJtdrtOr+LWTtmAaBWqbkl4BZiwmOI9Im0mHI/Na+UxMxivFNOoVv0KUG//oi2wnKYZKpXEN/2uYvYHkPp3jGE54eE35TJmcSasBaJNWEtTZmY2TRqa0IIIcR16lzBOVSoUFAwKSZ2pe5iV+ou/J38iQmPYXDYYJztnAl0c6hKstp7w4h+rNr0O3y2hMG/fY9zZhoAgdnnmfbTPJ5Y+xmb+9xBqvNLEN2VxMximSxECCFErW6KHrNffvmFl156CZPJxF//+lcee+yxeq8rPWbCWuTXPmEtEmuXl1Oaw7qkdaw7vY688jyLZVqNlv7B/bkj/A7CPcLN5al5pew+nQtGA92P7MDu0/kExe2t0XZclz783P8eim8bRBtfl5timKPEmrAWiTVhLTKU8RoYDAY6duzI5s2bcXV1pWfPnuzatQsPj1ruHaiFJGbCWuSiIqxFYq1uBpOBval7WZO4ht+zfrdYdlfEXTzWw/IHvs3xWRw8m0fPEDfCfZy4sH0fHX/8AvsVX6MpL7Ooe84zkF/6j2VT7+G4+3ny5IC2RIW6N/kxNQeJNWEtEmvCWmRWxmuwb98+OnXqREBAAE5OTsTExLB+/frm3i0hhBAtmI3ahr7BfXl78NssuGMBd0XchaOtIwAxbWMs6hbpi3B0yDcnZYFuDvS+cyBOyz4j4/gpNkx5iSx3X3P94JxUnlk5l89njmP44n9xbMsBoKrn7bsD51m0NYnvDpyT2R2FEOIm0+ITs23btjF69Gj8/f1RqVSsWrWqRp358+cTGhqKTqcjOjqaffv2mZdduHCBgIAA8/uAgADS0tKssetCCCFuAAEuATzW4zGWj1nOjNtmEOASYLF8/en1vLXzJdanfsSZwgMYTIY/1m0dSIcP3uT4tkPkfLmC8tsGmJc56ku5d+ePTJ4ynDO9buOHfy5ixZ4Uvtp3ji/3nK0aHimEEOKm0eITs5KSEiIjI5k/f36ty1esWMG0adN4/fXXOXToEJGRkQwfPpysrCwr76kQQogbmZ2NHb0CelmUKYrC2qS1ABzLPsbsXbOZvGoynx/5nKySqutQoJsDgzr54fngeHRbt5CxYx+/33EfFVqduZ3WB7bzlw9f5KM3HmDM9h8x5BWQV1JhvYMTQgjR7K6re8xUKhUrV65kzJgx5rLo6Gh69erFvHnzgKoxxkFBQUydOpXXXnuNXbt2MXv2bFauXAnACy+8QO/evZkwYUKt29Dr9ej1evP7wsJCgoKCyM3NlXvMRJMymUxkZ2fj5eUl4+NFk5JYazwGk4HYpFhik2JJLUy1WKZCRZR/FCPajqCnX0/Uqj/OdVpeGWcSzqH9Yjmtv12Oz8UMi3VLdQ5sjo5h+7D7KAoOo2tgK0Z28SPArY4HYrcwEmvCWiTWhLXk5+fj4eEhk39cmphVVFTg4ODA999/b5GsTZo0ifz8fFavXo3BYKBDhw5s2bKlXpN/zJw5kzfeeKNGeXx8PK6urk1xWEIAVReVgoICXF1d5aIimpTEWuNTFIWTF0/y2/nfOJB5AJPJZLHc096Tqd2nEuYaZlGeXqjnUEo+QXu20vPXb/DYt7tG2zva9GRVv7upGDiQVk52VBhMDGrnRqS/c5MeU2OQWBPWIrEmrKWgoID27dvLc8wulZOTg9FoxMfHx6Lcx8eH+Ph4AGxsbPjggw8YNGgQJpOJV1999YozMk6fPp1p06aZ31f3mHl5eUmPmWhSJpMJlUolv/aJJiex1jR8fHwY2GEgF8susuHMBtadXkdOaQ4AepWeziGdcdQ6Wqzj7Q2RbYNgSBf4+3OYjh1DNX8+pi++RFNWNflHv9MH6Xf6IKlrAvk2+k7W9hhGqckG91buFJZX0s7HucX2pEmsCWuRWBPWotVqm6ztq07M9Ho9e/fu5ezZs5SWluLl5UX37t0JCwure2Uru/POO7nzzjvrVdfOzg47O7sa5Wq1Wv5HF01OpVJJrAmrkFhrOp6OnjzQ5QHGdxrPgQsHiE2KxcvBC2edZQ/Xd8e/w97WnkGhg/5I2Lp2hYUL0bz7LixZAvPnQ3IyAIHZqUz75d88vWEpBwfeyQn9ZI44+vLT7xeYeEtoi51yX2JNWIvEmrCGpoyvBidmO3fu5OOPP+bnn3+msrISV1dX7O3tuXjxInq9ntatW/PEE0/w1FNP4ezctMMsPD090Wg0ZGZmWpRnZmbi6+t7mbWEEEKIpqdRa4gOjCY6MJpL7xoorSzl2xPfUm4oZ/mR5QwIGcDI8JG0dmtdVcHNDV56CV54AX79lYuz3sd9z3YA7PVl9Fu3gn7rVnCwQzTfRN/J29l96Rzkjq1Gxcgu/i02SRNCCHF5DUr57rzzTu677z5CQ0NZv349RUVF5ObmkpqaSmlpKYmJifz9739n06ZNtGvXjg0bNjTVfgNVXYk9e/Zk06ZN5jKTycSmTZvo06dPk25bCCGEqC+VSmXx/lD6IcoN5QCUG8pZd3odf1n7F15e/zKbzmyiwvi/GRk1GrjzTkrXrOXzxb+wb8R4KnV/DFvseXIvs5f9Hx+/8SDOi/7NjgNnWLhNnoMmhBDXowb1mN1xxx388MMP2Nra1rq8devWtG7dmkmTJnHixAnS09OveQeLi4tJSkoyv09OTiYuLg53d3eCg4OZNm0akyZNIioqit69ezNnzhxKSkqYMmXKNW9bCCGEaAr9gvsR6BJIbGIsv6X8Zk7SEnITSMhN4LPDnzE4bDAx4TH4O/sT6ObA7fcMIrFfL47pZ5E9dwGRP/0Xn5wLAATnpvFq7AKe+205G3uNYM/IB/B0GkCgm0NzHqYQQogGuKpZGY1GIzt37qRr165NPiHGli1bGDRoUI3ySZMmsWzZMgDmzZvH7NmzycjIoFu3bsydO5fo6OhG2X5hYSGurq7k5eXJ5B+iSZlMJrKysvD29pbx8aJJSay1LGWVZWxJ2cKaxDWkFKRYLPNz8mPhqIU1etxS80pJvFBAlyM78Fy6CDZurNHu+V792TtqAvsjetPG15UeIW4UlRsI93GyWsImsSasRWJNWEt+fj5ubm4ta7p8nU7HyZMnW+RkH41JEjNhLXJREdYisdYyKYpCfE48sUmxbD+3HYPJwOTIydzT8R6LekX6IpztLO/hzth9EOPcefiu/tY8m2O1c+7+fHfLXcQPH4uzryfB7g7c2zPQKsmZxJqwFok1YS1NmZhd9ayMnTt35syZMzd8YiaEEEJYg0qlooNXBzp4deCxHo+x8cxGBocNtqiTVpjGs2uepXdAb0aGjyTSJxKVSoVvn57QZynkf0TSu3Nx/WwhXtXDHC9e4KU1n1K6cRk7+o5ky9DxrLHV4OaoJSWnmLJKo0wYIoQQLcBV95itXbuW6dOn89Zbb9GzZ08cHS2fzdLYGWRzkR4zYS3ya5+wFom169d/Dv2H1Qmrze/9nfyJCY9hcNhgcy9aal4pu09l4fzbOrqv+hKffTtqtHOs8y2sGXgP33t3AZWKgRE+xHTxa/RhjhJrwlok1oS1tMihjH8O+j+PfVcUBZVKhdFovPa9awEkMRPWIhcVYS0Sa9evlSdXsjJ+JXnleRblWo2W/sH9iWkbQzuPdpb3pJ04QfEHc7D76ktsy8ss1kv1COCHW+7k0O1jKNI54OGo5ckBbRut90xiTViLxJqwlhaZmG3duvWKywcMGHBVO9TSSGImrEUuKsJaJNaubwaTgb2pe1mTuIbfs36vsbx1q9Y8HPkwPf17WpSnpVygdMF/CPjvEhxSz1osK9Pq+Ln7MFb1GYNXdCQTbwklOacEUOjTxvOqe9Ek1oS1SKwJa2mR95jdKImXEEIIcT2xUdvQN7gvfYP7klaYRmxSLBvPbKSksgSAM/ln0Bv1NdYLCPWHd2eweeLjpH39I/1jvybk0E4A7CvKGb/3J8bv/Ym49r3YPuJ+4rrcioNOi6eTTqbdF0IIK2hQYnbu3DmCg4PrXT8tLY2AgIAG75QQQggh6hbgEsBjPR5jYteJbDu7jdikWHLLcukd0NuiXkJOApklmdwadCvh/q7w0Dg0L02B9BSKP5iD7pv/YlNaNZtjt/j9dIvfT45PEL/f9SD71HeSlldKTkkF/dp6yiQhQgjRRBo0lNHHx4cxY8bw2GOP0atXr1rrFBQU8O233/Lxxx/zxBNP8PzzzzfazjYHGcoorEWGYQhrkVi7seWX59NK18qi7J/b/snetL242rkyrM0wRrQdgbej959WyoelSzHM/QSblGSLdcu0Ojb0Gk7sgHvwu6UHHfxcyCup6pFzc9RecaijxJqwFok1YS0t5h6z3Nxc3n77bZYsWYJOp6Nnz574+/uj0+nIy8vjxIkTHD9+nB49evCPf/yDkSNHNurONgdJzIS1yEVFWIvE2s0lpzSHR1Y/gsIfl3sVKqL8o4hpG0NP/56oVf+LA6ORnO9WUfDeh7Q5vKtGWyc7R/P1LXexo21vnB21BLs7cls7Lzyd7Gqd0VFiTViLxJqwlhaTmFUrKyvj119/ZceOHZw9e5aysjI8PT3p3r07w4cPp3Pnzo26k81JEjNhLXJREdYisXZzURSFo1lHiU2MZXfqboyK5azJ3g7ejGg7gmFthuGqcwXguwPniVu3izG7VtF980/YXPLQ6vPu/qwbMJZzd47H2deL+IxCQjwceKRfa4vkTGJNWIvEmrCWFpeY3UwkMRPWIhcVYS0Sazevi2UX2XB6A2tPryWnNMdimY3ahkWjFuHl6EVqXimJmcWE+zhxJukChs+W0G31F7hnpFqsU25nz2+9h/Nd9F1cDGlLv7Ye2NpozPeiVcdapa0zSdkljf6cNCGqyeeasJYWlZiNHTu2XvV+/PHHq9qhlkYSM2EtclER1iKxJkyKif1p+4lNiuVQ+iEUFCI8Inh/2PsW9RRFIS2/jMTMYpy1arTr1xHy1We4bt9co81jnXqzdtA4fvLtgpOjPWO6BxDT2Zec3By2pJSTV1bJoAhvBrX3rrGuENdKPteEtbSo6fJdXV0bdQeEEEIIYV1qlZrowGiiA6PJKM5gXdI6wj3CLeooisLL618mzC2MkeEjae3WGp56sOoVHw/z5mFcugxNadU0/Z2P76Pz8X3c7+7HN71G82NeDPuSc2nvacuFEoUivYHEzCLpNRNCiMuQoYx1kB4zYS3ya5+wFok1UR/Hso4xfdN08/sIjwhi2sbQP6Q/Wo22qrCgAJYtg08+gdOnLdYv1eqI7TaENf3HUNimPcXlBtyctLT3dcHXxa7OGR2FaAj5XBPW0qKGMt5sJDET1iIXFWEtEmuiPjad2cSCgwsoN5RblDtrnRkcNpiY8Bj8nf2rCk0mVs36DyFfLaH7ib012joQ3oO1g8aR0LM/hRUm9AYTLjpbxkUFMi6q/s9HFeJy5HNNWIskZs1IEjNhLXJREdYisSbqq6yyjC0pW1iTuIaUgpQay7v5dGN0xGh6B/TmQMpFdiTlMER1kc4rv4Tly6G42KJ+rncAP/Ubw5qoGIyurrT1cqattyMFZZWUVRoZ2cUfX1edeeIR6U0T9SWfa8JaJDFrRpKYCWuRi4qwFok10VCKohCfE09sUizbz23HYDKYlw0MGchLt75Uc6WCAkxLl2L6+GNsUlIsFuntdOy+dSTf9xlDklcwBWWVaIAOAS4EuTlgMCEThYgGkc81YS1NmZhJ5AohhBDiilQqFR28OjCtzzSWj1nOlG5T8HX0BWBk+EiLunqDnriMOBQXF3j+eXJ27sT088+U3z7EXMdOX87AzT8y752Hmb3oFe48ewBvR1tK9EbO5pbi7qgl3MfJot3UvFI2x2eRmmf5TDUhhLhRSI9ZHaTHTFiL/NonrEViTTQGRVE4nn2cTl6dUKlU5vKNZzby8d6P8XfyZ3ib4XR16krrwNZVsZaQAPPmVU0Ycskwx9KAYHYMG098zL3ovD3M5dWThCRmFnPwbB49Q9ykJ03UIJ9rwlpkKGMzksRMWItcVIS1SKyJpjRt3TQSLyYCVcmbYlAYEj6EkeEjaefRriqJKyyEZcso/WAODueSLdbX2+nYdksMX0aN4rRXCB6OdtzRxRc3RztAIczTiaJyg7lHTe5HEyCfa8J6JDFrRpKYCWuRi4qwFok10VQURWHX+V2sSVzD71m/oygKFfoKtHZaVCoVrVu1ZmT4SAaEDkBnoyM1t5gDC76m04/LCT+0s0Z7+9t05/tbx3Ch32DCfFzpEuDKyfRCTmYU0sHXhQ5+zpzNLaNniBvhPk6SpN3E5HNNWIskZs1IEjNhLXJREdYisSasIa0wjV8Tf2XNyTUY1AaL4Y4Otg68cusrRPlHkZpXSmJmMR0KL+D0n4Xo/vsFNv97aHW1dHc/tg8dR8Y9E9iUWUFhWSVujloctBr8XR0Y3yuIonKDDHW8icnnmrAWScyakSRmwlrkoiKsRWJNWIvJZOJ8+nkSyhJYe3qteYijWqVmyZ1L8HDwqLnS/4Y5Mm8eJCZaLNJrdWy/ZQRH7nqIeI8gTmUW4+OiY1xU0P9qKPLQ6puUfK4Ja5HErBlJYiasRS4qwlok1oS1XBprSReTWJO4BoPJwLQ+0yzqrjy5kqKKIka0HYG3ozeYTLBuHeUffIRu04YabSd27s1vQ8ZTNGQEWaWV5JZUEB3mjpujHXklevOkIZKk3Rzkc01YiyRmzUgSM2EtclER1iKxJqzlcrGmKIrF0EaDycDkVZMp0BegQkWUfxQxbWPo6d8TtUoNp05R9MEc7L/8vMYwx7KAIH7qO4a1vUfiFexHQkYhheUG3By1BLnbM/GWUHxddew+nYv0qN245HNNWEtTJmY2jdqaEEIIIUQd/pyUASTmJlJcUTV9voLC/gv72X9hP94O3oxoO4JhbYbhuvDfMPtdWL6c8g8/RpdyGgD7tPPc9+0n3L36PxzqP5KlPUZR4h1Cfome/NIKvtiTQr+2nmxNyEGlAk8nXY3ErPo+N5k4RAjRnKTHrA7SYyasRX7tE9YisSaspSGxlleWx4YzG4hNiiWnNMdimY3ahlsDbyUmPKbquWmKAuvXw9y5EBtbo63krtGsHTSOre1708rRHv9W9tjbqsku0tPW25keIW4WU+5/fzCViyUVDIrwlolDrlPyuSasRYYyNiNJzIS1yEVFWIvEmrCWq4k1k2Jif9p+YpNiOZR+CIU/vqY4a51ZNmYZWo3WXJax/wiVn8zDf+U3aC59aLV/EOsHjeXA7WPxDPYlKbOYskoDTjobNGo1we4OONiq2XPmIqGejjzSL0x6zK5T8rkmrEWGMgohhBDipqBWqYkOjCY6MJqM4gzWJq1lw5kNFOoLGdJ6iEVSBqDp6I/v54uh8AP4/HMqP56LbVLVbI4OF84z5r8fM/K7BWTcOY5Ng8ex2uBGSbkBRQ0qwNXeFkc7Gzr4OUtSJoRoVtJjVgfpMRPWIr/2CWuRWBPW0lixVmmsZOf5nXTw7ICPk4+5PL88nymrp9DGrQ0xbWPoH9KfnQkXyV35C4PWr8Bj28YabcW17c6q/mPJHDAUP3cnfF3sLJa7OWoJ83QyD3WUZO36IJ9rwlqkx+wanD9/nokTJ5KVlYWNjQ3/+Mc/GDduXHPvlhBCCCHqyVZjy8DQgTXK159ej8FkICE3gYTcBD47/Bk9fPoTMrIvZc9MgOxUij6Yg+6/X2BbUjXMsVvSYbolHaZwzQKS73uY7f3vwtDKjd9T8zmTXYyrvS09Q9wxmBS2J2bTwc9ZZnIUQljFDd9jlp6eTmZmJt26dSMjI4OePXty6tQpHB0d67W+9JgJa5Ff+4S1SKwJa2nqWNt2dhvfHf+OlIKUGsu6+XQjJjyG6IBodh4+S+WSpfRZ8zUO/5vNsVqlnY6U4WP4b+/RbLfzw0lnyx1dfCmtNLE3OZdSvYGeIe7m+89kBseWST7XhLXI5B+NKDIykl9++YWgoKB61ZfETFiLXFSEtUisCWuxRqwpikJ8TjyxSbFsP7cdg8lgsdzd3p3hYffiZxdNuJcDgQd2Vs3muGZNjbaSu/TmyF0PcbTnbUS18WZ/ykUOnr2Io50NvcM8uLdnILtP5xJ7NJ1QT0dGdvGTIY8thHyuCWtpysSs2SN327ZtjB49Gn9/f1QqFatWrapRZ/78+YSGhqLT6YiOjmbfvn1Xta2DBw9iNBrrnZQJIYQQomVTqVR08OrAtD7TWD5mOVO6TcHX0de8/GLZRdwdbRnU3ptADycYPhx+/ZU9sbvZPeoh9A5/jKAJO7qPMf98nicfHYHT3A95tJMrd3Txx1GrIT69kCU7ktmfnEtuiZ6zuSXsSMrh4Nk8EjOLa9s1IYRokGa/x6ykpITIyEgeeeQRxo4dW2P5ihUrmDZtGgsWLCA6Opo5c+YwfPhwEhIS8PauetZIt27dMBgMNdZdv349/v7+AFy8eJGHH36YxYsXX3F/9Ho9er3e/L6wsBCo+iXGZDJd9XEKUReTyYSiKBJnoslJrAlrsXasOdk6MSZiDHe1u4vDGYeJTYrlWNYx+gf1t9iH5Lxkjron4/vP18l2nY3/L9+jmjcPVUICAN4XM/D+z/sYvpjH4Ji7qRh4D6e8wjiZXkBJhZEIb2faelc9Aw0byC4q53xuCQFu9lY5TlGTfK4Ja2nKGGtRQxlVKhUrV65kzJgx5rLo6Gh69erFvHnzgKqTERQUxNSpU3nttdfq1a5er2fo0KE8/vjjTJw48Yp1Z86cyRtvvFGjPD4+HldX1/ofjBANZDKZKCgowNXVVYZhiCYlsSaspSXEWpmhDHsby4Rp8dHFbE/djo3ahlv8buH24Ntp4xyG3bZtOCxZgm5jzdkcL/aM5pcBY9nYphddg90orzRxobCcIr0RRYGBbd0Y1ckTgPRCPcm55YR56PC7ZNZH0TRaQqyJm0NBQQHt27e/+WZlrKio4ODBg0yfPt1cplarGTJkCLt3765XG4qiMHnyZG6//fY6kzKA6dOnM23aNPP7wsJCgoKC8PLyknvMRJMymUyoVCq8vLzkoiKalMSasJaWGGvlhnLiLsahtat6Htq+nH3sy9lHa7fWxETFMOCe1aTHJVL04ceE/vI92pIiANwP7uXhg3sZ5xfAqXseZk3vGGxsHTHoyzGawNnZ2TySZ+u586yLzyfE3ZFH+nlKT5oVtMRYEzcmrVZbd6Wr1KITs5ycHIxGIz4+PhblPj4+xMfH16uNnTt3smLFCrp27Wq+f+2LL76gS5cutda3s7PDzq7mr1tqtVr+RxdNTqVSSawJq5BYE9bS0mLNQevA3Ji5xCbFsvHMRkoqSwBIzk/m3wf+zbIjy7g99HZGLnwDrfrjPx5anXgKAPv0NCLnzaKzbg4XRt7NrwPuQR0ZSRtvZ7aeyiHcxwm1WkWx3si5vFL2JF/EM9uOcJ+qoY8yo2PTaWmxJm5MTRlfLToxawz9+vWT8cZCCCGEMAtwCeCxHo8xsetEtp/bzprENSReTASgtLKUXxJ/4ZfEX/hg2Ac4TJjC9+GDMa5fz/BN39HpyE5UioKmvIygH7/iqR+/Iq/XraQ+9Bhb2/Ymp1gPqOgV6kZ2kZ4tCVmUVxoZ0dkXTycdB8/mAUhiJoSooUUnZp6enmg0GjIzMy3KMzMz8fX1vcxaQgghhBB1s7OxY0jrIQxpPYTE3ERik2LZenYrFcYK/J38CXcPZ0tCNhfLDNgMGMyx8aPw0JTg9+USTJ8tQV1UNUGY2/5duO3fRYCHL9uG3Mtv/e7EM8SP0goTqXml2NloABXOOhtKKwwkZhZJr5kQooYWnZhptVp69uzJpk2bzBOCmEwmNm3axHPPPde8OyeEEEKIG0a4RzjhHuE80v0Rfkv+DWetMyqVyjwEMdzHiU8Pvc0pGztiXp5AyYPPYlj2BX1iv8bxTFVvm3tuBmNWzCPmx0WcGTaG8w8+SkqX1v/bgkJyTjFZhXqyi/S4OWrxdCrGWWdDUbnB/K8kbELcvJo9MSsuLiYpKcn8Pjk5mbi4ONzd3QkODmbatGlMmjSJqKgoevfuzZw5cygpKWHKlCnNuNdCCCGEuBE5aZ24M+JO8/tANwcC3Rw4V3CO37N+B2D/hf042rgTcVd//P9vCzYbd8Mnn9D2wDbUioJdZQUdfv2WDr9+CwMGsGvkAyz16IKbiwNdA6tmcTuZXoDBBO6OWgxGBRuNinMXSzGaTEy8JZSoUPdmOX4hRPNp9sTswIEDDBo0yPy+ekbESZMmsWzZMu677z6ys7OZMWMGGRkZdOvWjbVr19aYEEQIIYQQoqnklObg6eBJTmkOACWGixzKWc3v237l1ta3EvPLPDLOKxg/mU/Aj1+bhzmydSu3bt1KuJs3a/qPpfDBh0ky2aGvNNHez4UIH2f2p1zE3lZDUVkFGYV6diTlSGImxE2oRT3HrCUqLCzE1dWVvLw8mS5fNCmTyURWVhbe3t4yo5RoUhJrwlputFgzmowcuHCA2KRYDqUfQsHyK1SwSzB3tLuDGN/+nJr9b1w/W4DvhRSLOhW2dmzqMZjNQ8cz/tHRFJUb+OFgKioVBLs7cCQ1D1d7LaO6+qOz1ZiHNqbmlcqMjldwo8WaaLny8/Nxc3O7+Z5jJoQQQgjRUmjUGqIDo4kOjCajOIO1SWvZcGYDhfqq3rFzhefYl7aPkeEjcXxxKttHP4D3vu30/vm/6NavRaUoaCv1xOxdQ8zeNZxdGUXe+EmE9hxAVqmR7CI9heUGUnJKSMwqorWnE+39XOjX1pMdSTlcLKkAZEZHIW5U0mNWB+kxE9Yiv/YJa5FYE9ZyM8RapbGSned3siZxDSdzTvL3/n8nOjDavNykmNh+djt9KrzRLlgMS5ZAQYFFGwWevmy5/V5+6zcaO18fTmUWUlhuwMvFjoBWDhhNJjRqNa3sbeng50yfNp7m5Ky6J+1mnzzkZog10TJIj5kQQgghRAtkq7FlYOhABoYOJCU/hSCXIIvlBy4c4P3d7+OsdWbwQ4OJeXU//is3UjlnLran4gFwzcngrm/nMWr1YsrvvY+UCY+wQRtAhI8zCZlFnLtYSit7W0DhaFohnk46c/KVmFnM5oQsCsoqcLXXAtKjJsT1Sn5SEEIIIcT/t3fn8VFX9/7HX5N1sjPZQxIS9kUgSFhkE1AUgmJxAWqtgvuuvVTvr7a3btft3tqWFm3rerFW64KC1QZQEQUUWcImCCHBJCQh2ySTTNZJJjO/P0LGBMKezJDwfj4ePurMfOc7J/RjwjvnnM+RTpDcKxlvL+92z6VnpQNQ3VjNysyV3LluMb8dfJhtn71G8QcrMU+/HKfBAIC3zUbQW3/ngiumcfdjt5L4RTpDIgLoFeBLTYOdyno74UF+DIwJpsBSx7r9LYdXV9U3Ymty4ONlwFzTQIGlzu1fu4icPc2YiYiIiHSRnw7/KaH+oWw4tAG7ww7AzpKd7CzZSURABDP/tIjLfZ4h4tW34bXXXMsc/b/ZyPBvNtInKo7G6dfw7/FX4IiMoMluJH33YYqtDa52+2EBfoRH+hHo6836Ay1dI+eN6eOxr1lEzoz2mJ2E9piJu2h9vLiLak3cRbX2I6vNyuc/fM6qrFUU1xa3e83L4MU9Y+5hZuwkePNNWLoU9u1rd43d149NF83kX1OuIS9xECFGH0Yk9HItd5w8IJIccy2rvisiOTKIWyb3PeGSxp7W5VG1Ju6iPWYiIiIi3ViofyjXDL2Gq4dczY7iHaRnpbOlcAtOnDicDoZGDYXgYLj7brjrLli7tiWgffwxOJ34NDUyZcPHTNnwMT8MvZDvrl5IVtQlfLi9ktAAP6ob7EzoH8G+Iiu55bX8c/MhfH28mDwgktgw4zEhLKukhow8C6A9aSLnCgUzERERETcxGAyMjhvN6LjRmOvMrMleQ4G1gD5hfdpeRHpSI1senMSQW3/O7DXrCX3rTdcyx377dtBv3w7KekWx4qKryL36ekKMfcgqqSE21EhZtY0DJVaKrTb2Hq4k0RSI3QHmGhtQjqXWBkBSRAADY4I98KcgIh1RMBMRERHxgMjASG4YecMxzzudTv6V+S92Ff3Ae3VNvD9pAHfcvYypG/LxXvIXVzfHqMoy7lj9Go4v/kHJlVfz2SXzMY0fwzWjE2hoamb13iLyK+ootdpITQoHnHyVaaa0uoGYUCPXjE7QbJnIOUTBTEREROQcUlxTTGVDJcF+LX9NszYV8sJ3r/F6VCCXvPUg437wJ+Gld4lc9ykGpxOvRhtxH77DTR++g+2iiRT8/Db+3X8cY5PCqbM1U2ezE+Drxb6iapIiAhmZEIrpSHfHtgosdWw62DKjZgrya3demoh0PTX/OAk1/xB30cZlcRfVmriLau3M2ew2NhzaQHpWOlkVWce8PjxqOGlBKUz8YAs+rx57aLW5VzQbLr2WLy/+CRF94wHYXWBlZEIYUwZGMTAmmOKqBtK/KyI21MjoJBMbs83sLqikpsHumlGbPiTaLV/v2VKtibt0ZfMPBbOTUDATd9EPFXEX1Zq4i2qtc2RXZJOelc5XeV/R2Nzoet7P249lP1mGtayBmtfeoN8/X8c3s303xyZfPwpmzaXuzrv5wBFFTYMdo583I+LD2Jhdxs5DlcSEGpk4IJKK2kZ8vAzEhvp3OGPW2skxxOhDdYP9nOroqFoTd1FXRhEREZHz1IDwATww/gFuvfBWvsj5gvSsdAqqC5jSZwoh/iFsq6kn46I5pM6/kQG564h/6Z94/aulm6NvUyN9P34PPn6P6FFj+eKyBWRNuJStOeXkV9SRGB7AxQOjGZ1kIsdcCzhdgaz1EOvWANbaydHH24C9ueX3+udKMBPpCRTMRERERLqBIL8g5gyew5WDrmRP6R5MASYA116xxAgffrnnQ0JujmTWg0u5PD2TsFffhMpKAKJ2bmXBzq3URceyavLVlF90BbPGjWTemEQAqhvsZORZiAyucQWxdZml7Cqo5LrUBAbGBGOusbXsQevlR4jRp11wE5Gzo2AmIiIi0o0YDAZGxIxwPU4wBZJgCmR19mrq7fXU2+v5e91q3h7jw8TZDzExo4aRL31ISPYBAAJLi7n2w78y95PXabh2HiV33MX64D5Yam2EGr3JKrFirmkg2N+XqvpGam121zlohZX1VNQ2YgryZ2O2mYraRtcYoOcdXC3iTgpmIiIiIj1AQmgCqXGpbC/ajhMndoed9cXfsj4e+iy5lLS6m5j+z00ErUwHpxPvRhtB//wHQf/8B6MGjmTDrOupmT2HA+U26pvsBBt9sDU5qHPa2ZZbwYasUirr7fQJDwScVNQ2En5Ud0cdXC1y5tT84yTU/EPcRRuXxV1Ua+IuqjXPKK4pZnX2aj774TOsNmu714w+RuaGT+SG1Yfh1VddyxxbNUTH8c3l17Fm4lXk+wQR5OdNsxNqGuyEGH1IighiaFwIfSODO2wA4qkZM9WauEtXNv9Q5YqIiIj0ILHBsSwatYhlP1nGLyf8kqGRQ12vNdgb8InpDb/7HRQUYPnDUszJA12vG0uLuOQfS3n6wSt44M1nmNVYxEV9I0iOCGR83wiGxoXwXaGV9O+KMNc0tPvcE4Wy1kYiBZa6rv3iRboxLWUUERER6YF8vX2ZljyNacnTyK3MZVXWKjYc2sDl/S9vuSAoCNN/3EfGdWks/egP3LQ2i37/WovB4cCnqZGLNnwCGz6hcvQ4Nsz8KSHXz2dAgonCygZ2F1RSVm0jMtgIwKaD5ewrqsLuAHONjcjg9gGtoyWO2o8m0p6CmYiIiEgPl9wrmbvH3s3tqbfj49X+r3+7zevZHnGI7fP9GXXTPczeXMG4l/+Nt6Xl0Ope27cwZ/sW6l/9Hxpvv5P5C28mvlcc4CTE6MPyjAI255RTZ7OTmmQCnGTkWTDX2IBywEnfyGCSIgIx1zRQYKlr134ftB9NBLSUUUREROS8cXQoczgdfJX3levxzoZcnkmxcuvLV/LPJbdSPnqI67WAshLCnnmS3iMGM++F3zLPUEaOuYbvCirxNkBEsD9D48LoGxmMj7eBXHMt72/LZ/WeYqob7EQG+5NXXk9WSQ0AIUYf6hrtZJVUa4mjCApmIiIiIuctL4MXf077MzePupnYoFjX8+VNVbwdXcItDw3imWW38u28qTi8DC0vNjbCG2/AmDFMv/UaJmV8wdS+Jm68KJkJ/SOobrBjb3ZS39RMsL8PEUH+mGsaCDH6kJpkcnVxrG6wU2q18V1hlSusiZzP1JXxJNSVUdxFHaXEXVRr4i6qte7F6XSyo3gH6VnpbCncgpP2f0WcY7yaUW9/w4WffYBvVWW715rj4vC+5x644w4KfIPJKqkhxOhDdYMdc00DeeX1rlC26WA5llqb672mID8m9I8EOOM9Z6o1cRd1ZRQRERGRLmUwGBgdN5r/uvi/eP0nr/PTC36KyWgCIMw/jMsvvo7a/36G0r1Z8PLLNIwc5opu3kVF8Nvf4khIxHTP7UyvzWdMcviR2TEDSREBDIxpCWxfZZbx+b5Sviu0Ygryb9dA5IOMAtJ3F6mDo5yX1PxDRERERNqJDIzkhpE3sGD4AjYXbKbB3kByRCjJEUdmCG6/ncf6FJL//Tau+baMK1ZsJaDJiVdTI0HvvA3vvM3hYReyY84NbBw2mcnD4lyzYFMHR2GptWEK8qO1UUgLJwYDFFvrsTbYXWNR50Y5XyiYiYiIiEiHfLx8mNRn0jHPl9eVs/HQt1i8bOyaFMRzY6cyJ9fBz1fsoP/hagB6f7+D3t/vYIopioL5N3E45F6ynEFM6B/RrmU+lGOuaaBvZMvsWmtoa+34WFHb6PpchTTpyRTMREREROS0VNmqGBY9kD2lmfh4eWEPcLBxrA9rho8lMbeJn3+VS9qWfHwc0MtSRq+Xfo/j9aVYpqax/8bb2DQsBXAyoX8kkcH+ZORZiAw2Ehnsz3eFVRRbbewrslJZb6dPeKBrb9pXmWVMHRzFvDEKZtLzaI+ZiIiIiJyWfqZ+vPKTpbx57V+YN3w2poBAahrtePv6cqi/kT/fNZxFL8zg77ek0uTd0s3Rq6mRCz7/iBkL55D6syupeeMtsgsshBh98PE2EGL0YWBMMOFBfuwrtpKRZ6FXgC+DY0J4fWMOX2aWUlFnY19RlfafSY903gSzuro6kpKSeOihhzw9FBEREZEeYUD4AB4Y/wD3jfojQ0OuxuQfS2SwP0Y/b6p6Gdk5/2K2rtnKZ1cupDY4zPW+flm7ufmFXzP+ktEYn3saP3MZ1Q12EkyBXJeawNDYUCKD/RkaF0JmSTVr95Ww93AVQX4+2B2csL1+gaVOzUOkWzpvljI+/fTTXHTRRZ4ehoiIiEiPMzI+hgCfaxkQfROVTT+QnpXOpoJNpA1Io0/4UDY99t+s+X+PMHXb52xN/z0T1ucQZoMAcynDX/oDQ19fyp7Js/j+wQcY9pMZ3DK5r2s/WXFVA3sLq6iz2RmbbGJgTKjrLDRoCWKZRVbsDdVUHrKRWVKN3dHymvaiSXdyXgSzrKws9u/fz5w5c9izZ4+nhyMiIiLSoySYAl0hKJERjIgZgaXeQpBfEH7efq49YeviankicACmK+KY9F0lV32yj+ElTrybmkhZ9zGs+5iqlFQC7ruP6Tf9DPz8SDAFEhtmdAU1aGmtD2Ym9I8kq6SGf393mMzCSpoN3oQH+zGub0S78CbSHXh8KeP69euZM2cOvXv3xmAwsHLlymOuefHFF0lOTsZoNDJ+/Hi2bNlyWp/x0EMP8eyzz3bSiEVERETkZEwBJvy8/do99/6eT6iqb8ISGMS3l/bj109fwn3/dSEfXRhErW/LNWG7Moi4/WZIToYnn4SSEhJMgUwfEk2CKdB1Ftr6A2bXQdYFlgZKa5tosDczJDaUyQNaAlvb5Yxa4ijnOo8Hs9raWlJSUnjxxRc7fP3dd99l8eLFPPbYY2zfvp2UlBRmzpxJaWmp65pRo0YxfPjwY/45fPgwH330EYMGDWLQoEHu+pJEREREpAO3pf6cqwZdQ2xIy8HVBAZwaFg8ry6+mEVPpbLkqjh+OPISRUXw2GPQpw/ceCNs3UqBpQ5zjY2kiACiQlpa6rfsTTPS12TkgrhQYkON5JhryMiztNuLllVSw7rMUpZnFCicyTnJ4HQ6nSe/zD0MBgMrVqxg7ty5rufGjx/P2LFjeeGFFwBwOBwkJiZy//3386tf/eqk93zkkUf4xz/+gbe3NzU1NTQ1NfHLX/6SRx99tMPrbTYbNpvN9dhqtZKYmEh5eTm9evU6q69P5EQcDgdlZWVERUXh5eXx35lID6ZaE3dRrcnxNDU38U3BN6zKWsX35u/bv1heztyMRm59cycGh6PdS1UpqWyYuYCDF8+iyduHxPAje8icTqzV1ewoseGFgeHxoZRU2YgNMzJ7RBzxpgAKLfUszyjAUtfI1EFRDIoJ4UBJNYNiQog3BQBQaKk/5jmRtiorK4mIiKCqqorQ0NBOvfc5HcwaGxsJDAxk+fLl7cLawoULqays5KOPPjqt+y9btow9e/bw/PPPH/eaxx9/nCeeeOKY5/fv309YWFgH7xDpHA6Hg6qqKsLCwvQXGOlSqjVxF9WanIr86ny+OPQFGw9vxGZv+eX47Pj7ceZ4Me7T5Vz46QoCa6ravccWEcXBuQvYMfNasr1DuCAmkEi/Jg5U4qq1b3OtGAyQNjSCiX3DKLLayMivprLeTq+AljYLhVU2RsQFu17/995yqhqamJDci4l99fc+OVZVVRVDhgzpkmB2Tjf/MJvNNDc3ExMT0+75mJgY9u/f3yWf+cgjj7B48WLX49YZs6ioKM2YSZdyOBwYDAb9Zlm6nGpN3EW1JqciOjqa1P6p3Nd0H1/mfcnukt1cM3Q6WQk1+F12EZt/8yjVX/yJLRn/ZPbXpYwvAP/yMoa99gJD//4SxbOugvvug36DmXxhS60VWuoJCTFTWdeE3cePJt8QKuxQ2VSHt58vh6pteBu8GJoYxdh+EUSbAthbUUqjwYfeEUEkxkSycn8FJVYbY5PC8ff10iyaAODn53fyi87QOR3MOtuiRYtOeo2/vz/+/v7HPO/l5aUfKtLlDAaDak3cQrUm7qJak1MV5B/EFYOu4IpBVwDQJ7K1q2IED5t92d97HLsmleOzJ49rNxWRluUkor6JuI8/gI8/oHH0aLz+4z/wmj+fxIggFkQEsW5/KRl5FqJCahkcF4qXlxchRh82ZpupqG0kKsRIYkQQAIPjQqmoawKc5FbU8sW+Miz1jVTUNZJoCsLLy8t1basCS52rW6Ra858fuvJ72TkdzCIjI/H29qakpKTd8yUlJcTGxnpoVCIiIiLS1VpDT28TVNmqwABERGAeG8rvBiTxZnkJ07YXk7a7jpRi8Nu+vaVJyMMPw113wZ13MjCmZalZa3BqG542ZptpaGpm3f5S1+uRwS1NQ0KNPiRHBpFMENOHRGP09e6w/X5WScv1oDPT5Oyd08HMz8+P1NRU1q5d69pj5nA4WLt2Lffdd59nByciIiIiXebH0GPipStfYkfxDtKz0tlSuIVegREQH8E3Fwzmm8LDxO3LZ/bmCi47CEHFxfD44ziffhqfWVcRe8udbKoZQuu5ZwmmQKob7NibnWSWVFNR28iugkomD4h0dXwEiA41kppkYvqQaAC25VawPKOAyQMiGZMcDuAKazozTTqDx4NZTU0N2dnZrsc5OTns3LmT8PBw+vTpw+LFi1m4cCFjxoxh3LhxLFmyhNraWm6++WYPjlpEREREulLb0GMwGBgdN5rRcaMx15lZk72GNQfXYGmwQJ9EDicm8LeUUiZ8G03QB6uhuRlDUxOxH39A7McfEND/Ar6a+VOy71xEginQde+2yxo3ZpuxNztJimiZ+UqKCGgXuDZmm9mYZQYgNsx45JBrpyvsdURLHeV0eDyYbdu2jenTp7setzbeWLhwIcuWLWPBggWUlZXx6KOPUlxczKhRo1i9evUxDUFEREREpOc4eulhq8jASG4YeQMLhi9gc8Fm0rPS2VWyi5GDphH14HNQWAh//SvNL71MrrOc+GpIPriX5L/8luYPXoC77iLhrrtIGNKyLaas2sbqvUUMig4m3hSIuaaBvPJ6UpNMrs8vsNQR6OvNyIQfD6/+KrMMgwEig40kmAI7DGGtZ6ftKqjkutQEhTM5oXOqXf65yGq1EhYWhsViUVdG6VIOh4PS0lKio6O1SV66lGpN3EW1Ju5yqPIQJWUlpPZPddWavbaaW/86i4bMvVyyo4rZWZBoPfIGX1+YPx/uv58l1SY2ZpmZPDCSX8wY1GHAam0ikppkYmBMMOm7i8gurWZAdAizR8aRYApsd03r8scCSx3LMwqoqG1k+uBo1/OtNKPW/VRWVmIymc6/dvkiIiIiIieTEJqAX0P7NuZbKr6jIj6chqiJLOtfyvuH8xmzv4zZB5xMzG/C56234K23uC1lNIPTrif60p+33KvNTF2BpY5NB8ux1NpcSxuzSmrYXVCFwQADY0KAluAWYvRxBTfXuEyBXJea4ApfR1PzEGlLwUxEREREepzE0EQu63cZy/d8SrF3IPQZjLXfQDZfWEhs3mHS9jcyKxuid20nbdd2+L/nXd0ciYsDaLdk8ZrRPy5FnDo4CnC6glpGnsW1N81c09Bu39nxlmSCmodIe1rKeBJayijuoiU/4i6qNXEX1Zq4y4lq7UBpGa9t/ZgdpesobyiioqYRg9NBUkMlQYWHuOS7ahZvavMGX1+YNw8eeICCQSNO2uSjdTmiuaaBrzLNrhDXdtnittwKNmab23V0PPr9Ws7YPWgpo4iIiIhIG20DTe8w43GvGxQdxf9ccQtO5818nr2VZdtXcMCyHZ+YUMpje7O/bxI7HLmM3LoOb0czNDXB22/D22+TMHYs8x54oCWo+ft3eP/WGbECSx0th605j5kBa+3oaK1vorrBfkyDEC1nFFAwExEREZFuqG3Hw2svjMf3JNcbDAYuGziOywaOw1Jv4bMfPuPD7//NjDH3UXxFNBl7srhi40p8ly/jjf4WZh6EC7ZuxXDjjTT/8pd433VXy1LHI8scj5ZgCmTemEC25Vbw+sYcAny9SY4MZEL/SCYPiAQg0Nf7mBCm5YzSSsFMRERERLqdgTHB7CqopKK2kQMl1VxwZIXgqSwNNAWYmH/BfOYNm4fBYGh5ckQcXH8xL/9sJJ+sfZ7PCvLoX1hDWjZMzykl6MkncTzzDHsnXs6uuTfiP3kCEwZEHfMZG7PNrD/Qsi9tSGwokcFGpg+Jdp19ZgryPaZBCLQEzbaPW2mp4/lDwUxEREREup22HQ8HRAVBUzXQfmlg6+PjhRpXKGvjQO0eggf2pSGpD9uLS8kckM8bxaVMzYXZWXZGrE9nxPp0fug7jK1zf87qtKsIM4W49qBNHhCJtb7JNWPWGsKySmrIK68jKSLwyL41s+s9x1vO2Lbd/tGvSc+jYCYiIiIi3VLr/q6W5h8twazt0sAz2b/17KXP8nX+16RnpbPPbx/0iaOhvoE1ebmsGprH0KIm0rJgyqHv6ffHX1P56u/YNONa8n5xP4wYQI65lqFxIcc0C2kdV9smIWAgMrimw1b70BLmKmobCQ/yI8Tow7r9pR2GzNa2/idqUiLnPgUzEREREekxOmpP39H+reMtEfT19mVa8jSmJU8jtzKXVVmr+CL3CxqGDMFr4CAyDxeS2S8H21ors7OgV7WFtBWv4vx4GaUz55A39ifkDRhOZHBLQ5K2n3F0kxBwHnModUfj7ihkth1/27b+kcFGBbNuSsFMRERERHqkE50hdiqzacm9krl77N0sGrWIL3O/JD0rnVxvL/yTBzD1+rvgxVfggw+guZk6g53I9BU89O8VVAwdCQ/cz+6JM8koqnPd7+hZrQJLHZHBHR8+3Xb8BZY6zDU/HnJ99PgHxgS3O1tNuicFMxERERE575xON8QA3wDSBqYxa8As9pv3U1hdSFC/GXDxDCgogL/9jWXfLGFrWC0zs+Hyg7uJuPt2pkRFkXzdjfjddw+ZJbhmtVpmzE596eGmg+Ws+q6IyOCWlv0T+ke2G39rR0jp3hTMREREROS8c6LZtKO1XTY4NGooQ6OGtrlRAnWP/ZovP/iehkM/8HZsDu8MtzK+EGZnlZHy1z9geOXP9LpqLo4rbqBixIWAs90+MyjHUmvDFOR3nKDmpMZmp7zWRn1TMy170/zVqbGHUTATERERETmBky17rGmsYVTvVDY77TgTEnFYLGzKyWFT4mF6W2FWtp0Znyzn0g+XQ2oqFbfeiVfKdBx+frSGtNLqBmJCjR3uEZvQPxIwuMJb6960442ns6llv3somImIiIiInMDJlj0eKvMhqHEeD1w4n5LGLXz6w6dUhJugfhiH8/J4PSKPN1MamZIHd2RkEH7PHVwbHQ133MHh6xfB4ChX6Gr7GcfrtniyvWmtQSrE6EN1g/2sA9WZdLeU06dgJiIiIiJyAidb9rgx28zGLDMQyS9m3MCk+Dm8mfE5O0q/oLqfL8aBA2k6fJi9gfkEflve8qbSUnjqKXo/9xzzrrsO7r8fUidAm7PVju62CMc2EOlIa5Dy8TZgb3a6voYzdTr78eTMKZiJiIiIiJyFyQMi2/1vTlkDJWXJxHvdwvDkZrKqNrC7eSMJo+6lbH4/ot94BZYvB7udj/vZSVn1Dn3eeQdSU+GBB2DBAvD3P6bbYtugdqK9aa0Bqu2M2dk4nf14cuYMTqfT6elBnMusVithYWFYLBZ69erl6eFID9ZyOGYp0dHReHl5eXo40oOp1sRdVGviLudarbVdggiQV14Phiaamh0MiDIRGexPeGUp9W/+madql2FobGJ4KaRlw8R88ImIgjvvhLvugvj449637d60a0YnMDAmmE0HT9ZIpOPxag/ZqamsrMRkMlFVVUVoaGin3lszZiIiIiIinaht+/rW/WCts1fmmoYjywz9+OaiZCpqLybCWs6enBz2RFcRZoPLD5Yx649PEf3cc3DttS2zaBMmHHPftg1B2s6olVY34ONtYGO2mVkXxGH09T5h6Gq7hwwgfXcRxdZ6Zo/ozZjk8C7/85IWCmYiIiIiIl3k6GWAbYPaoNjrKbENYkvRWrJj4rCVmWkszOc9YwnLhzkZc9hO2oZ3SX3vXbxGp7bsQ1uwAIzG455dNvVII5GtuRX8UFbL6r1FhAX4saugkskDIskx13L0HrW2e8iySmr4/PsSLPWNhAb4nXYw0+zbmVMwExERERFxk/ZBLRzoyyLntby++Ss+bP6EQ/47sZoSMJmLaPIpZWvvJqbmwUPfZMCiRfDww3DHHXD33e2WObbeuzWsjU6qYGO2mcExIWSWVFNR28jGbDPZJTXUN9nZV1TN0LgQ+kYGH9O5ccawGIqt9a49c20dr1NkK3VwPHMKZiIiIiIiHmQwGJg5eBz9eg3Daajhnd2f8OWhT8lKrCKiupzBuQ1ATsvFZWU4n34a5/88h9c1R5Y5TpzYrpsjwJjkcNds14iEMFf7/PheAewrqiK3vJayahuFlQ3Ym51klVSTXVoDwPyxiYxJ7t/hWI9uQNLatr+j2bdWmkU7NQpmIiIiIiIe9uNMWjSXDH6AQxW38Mm+jWRathCw4FZKCw4Q/cYrON5/nx1Rdl6/sJm0ne8xffp7BI0Y/WM3R6PxBPduCWwFlgjXrFfrjNmGrFI2ZJWBAXqbAogNM3YYptp2iuzooOuOOjhqFu3UqCvjSagro7jLudZRSnou1Zq4i2pN3OV8qrXD3x/k8b/9jPyqHfg0NWG0w9Q8mJ0F8c5wym9YRM68m0gaOfC0QtC23Are25oPtMyYVTfYycizkBQRSGSwf4eHVZ9oJqztkseOlkt2V+rKKCIiIiIiRA9Jwu/yKVQVhhBaUYY9N5c1PlbW9IfB5RWkpf+BiS8tIX/STPbfdz9FF4xmYGzISQNR26WP0Nr1kTZdJNsfVr0tt2UP2+QBHbfkP/pw7OlDol331bLGjimYiYiIiIh0Ez5ePrxw5fPkVuayKmsV6Qc+w1yQT0DhIfYbysiMcPLaaAeX/rCKnyxchSluGHk33Mrmy+fg8Pc/5bPNWpckHt3uv3Xv2MZsMxuzzFjrmzqcDTv6cOxWWtZ4fFrKeBJayijucj4twxDPUq2Ju6jWxF3O51qrb6rnq7yvSM9KJ6d4H+Tl4czNw9DYyJ9WQ78jx5NVh/Tim0uuoen2O6mPieN4XRVPVeuMWaCvN9YGO6lJJtcB1ye6d3efMdNSRhEREREROUaAbwCzBsxiZv+ZZJZnkp6Vzsbc9fQraaRfVhls2wZASHUlfTe+jmntMg5dcCnrZy5g05WXHenmePr7wFqXPrYNWkcvXwSOCWEdNQfpSHcPcGdCwUxEREREpJszGAwMiRzCkMgh3Db6NiobKuHBRNi8GZYuxfneuyy5qJnCEAfjCz9j9suf0efdYaRfPI+MiTMpTIhot4fsVB0dtNouXzx62WJr2OqokcjRzsclj+dFMMvJyeGWW26hpKQEb29vvv32W4KCgjw9LBERERGRThfqH0qo/5FldhddBBddxN5HbiV/+V2Ql8emhEY2JUDv6u9J2/AEv1n5Z5rmtXRz7BOTeMaf2/aA67Za95i1hi0fbwMVtY3sKqjkutSEDoNXR+ehtdUTZ9TOi2C2aNEinnrqKaZMmUJFRQX+/v6eHpKIiIiIiNv07j+Kn17zGGsOpGPJ+R5ycjhMFa9dCG82W5iy/Y+kLf8T8VOvgQcehEmTjjm0Gk4vEB09m9YaskKMPmzMNlNR20hWSU27a9rev7WTY0eONxvXnYNajw9me/fuxdfXlylTpgAQHh5+kneIiIiIiPQs4QHh3DDyBhYMX8Dmgs2kZ6WzO/MryMmh8XARa/s6WdvXwRDzcv53ynIMo0a1HFp9/fXtDq1uG4gA0ncXUWytZ/aI3u3a7XekbVBre4B1W0ff/3hh6+gZtaySGtZllp5wFu5c5/G2NevXr2fOnDn07t0bg8HAypUrj7nmxRdfJDk5GaPRyPjx49myZcsp3z8rK4vg4GDmzJnD6NGjeeaZZzpx9CIiIiIi3YePlw+T+kzi6Uuf5m8/f5efXP8EQbPmwKBB4O9HXA0YAHbuhFtugcRE+PWvIb/l8OmBMcGuDoxZJTV8/n0JX+wvZcnnmfzn+zt5+auDbMutYN3+UtdZaB1JMAUyfUh0h4Gr7f0z8ixsOljuul+BpY51+0sB2r1/YEww4UF+rlm47sjjM2a1tbWkpKRwyy23cM011xzz+rvvvsvixYv529/+xvjx41myZAkzZ84kMzOT6OiW6c1Ro0Zht9uPee+nn36K3W5nw4YN7Ny5k+joaGbNmsXYsWO57LLLuvxrExERERE5V8WHxnPb6Nu4ceSNrM9bz6rMT0gr7g32D2DrVgBsFjPPffMs09/5HyakziXhgV+QMHmya5njjGExbM0tJ99Sz8GyWnLL6yi2NpBrriUy2J+xfU2n1Za/o66NrYdct+qoKUiCKZDrUhM6nIXrLs6pc8wMBgMrVqxg7ty5rufGjx/P2LFjeeGFF4CWcyoSExO5//77+dWvfnXSe27atInHH3+cNWvWAPC73/0OgIcffrjD6202GzabzfXYarWSmJhIeXm5zjGTLuVwOCgrKyMqKuq8O4NF3Eu1Ju6iWhN3Ua11HqfTicFggM2bMSxdymcZ77E0tRmAMBtcdhBm+V9A1O2/aFnmGBBAoaWef393mIOltQyIbglFa/eVYrM3kxgeyNUXxjMoJoQDJdUMigkh3hRwWmMqtNS73guc8X1OdN9TvVdlZSURERHn3zlmjY2NZGRk8Mgjj7ie8/LyYsaMGWzatOmU7jF27FhKS0uxWCyEhYWxfv167rzzzuNe/+yzz/LEE08c83xZWRmNjY2n/0WInCKHw0FVVRVOp1M/VKRLqdbEXVRr4i6qtS7Qty/84Q98vTEG+65/4Z1fQBWNLB8GH7CX1H/czqzfL2boZQvxX7iIuUPiYUhLcCqy2vBuDqWy3k6vAB/CfWxsPVDFd0U1VFUFY44wkpFf7Xo9NTGEuNDjN+fzBS4IB5qqoc2/l5ZWH/c9RVYbOeUN9I0wHvfeW3N+HJNv37BT+mOpqqo6pevOxDkdzMxmM83NzcTExLR7PiYmhv3795/SPXx8fHjmmWe4+OKLcTqdXH755Vx55ZXHvf6RRx5h8eLFrsetM2ZRUVGaMZMu5XA4MBgM+m2fdDnVmriLak3cRbXWdR69+nn2TFrEqsyP2bR1BY6cH3BWVrKtN2zrXU103gvMXPQXLh96JaH3LobJk4mONpAyoP19IiPqCQurds2c7Swuo9TaSHSoPyEhIWw+XM3u/CqCjT7MS00kNdl0VuPeW1HKD1V1hIX5kxLdcXfHsb4hrjFFt5kxO9FMmp+f31mN60TO6WDWWdLS0khLSzula/39/Ttsp+/l5aX/0KXLGQwG1Zq4hWpN3EW1Ju6iWus6KXEppMSlYBl/L5/98BmrN71JWeYOKDpMaZCTN0c4sO/5Fz+b9i9ISfmxm2PAj6EmMSKIxIiWc4QNXgam1sVgqbVhCmoJOl/sKyOrrBqDwUCepY5FE/pi9PU+4/b3g+NC8fLyYmBM8HFrou2Y2souq2VHfhVeXl7HvN6V9XVOB7PIyEi8vb0pKSlp93xJSQmxsbEeGpWIiIiIyPnHFGBi/gXzuW7YdWw7vI30He+xPeNjDDl5zMw+0qNh1y649VZqfvMwhkWLCLr7QejTp919jj6IusBSh6W2iah8P3LK66isbWL13iISTUGu60/3nLKOmogcrcBSx6aD5YCzXYOSkx1u3VXO6WDm5+dHamoqa9eudTUEcTgcrF27lvvuu8+zgxMREREROQ95GbwYFz+OcfHjKJ72EPuKdhNxWRksXQqbNwOwIrqCfx38A1Pn/5HZfS+n392/hilTOjy0OsEUyB1T+wOwLbeCjdlmBseEuGbM4Mfzzcw1NqDcNdt2Oh0fj5ZVUsNXmWUYDBAZbPT42WceD2Y1NTVkZ2e7Hufk5LBz507Cw8Pp06cPixcvZuHChYwZM4Zx48axZMkSamtrufnmmz04ahERERERiQ2OJXZgLAwEbrgBNm/GvvRPrGl4hwYfJ2v6OVnDGgY/vYY0Rz+mLPhP/G64qd0yx7bGJId3eFB1a0Az1zTwVaaZ0uoGQow+FFY2nPGB0gNjgpk6OApwtpsda3vItTvDmseD2bZt25g+fbrrcWvjjYULF7Js2TIWLFhAWVkZjz76KMXFxYwaNYrVq1cf0xBEREREREQ8bPx4Gi58mUkbUvhi499pyD0INhuZEZDJD7y2+i4ufeOXpE1aSO97/t8xyxyPp3VpYsuh1QYstTaKrQ2uA6VbA9TpLHk8ekllK08tZTynzjE7F1mtVsLCwrBYLOrKKF3K4XBQWlpKdHS0Ni5Ll1Ktibuo1sRdVGvnpvqmer7M/oz0NS+Sm7UFLJXtXh9VAg9GXknkPQ/BxRd3uMzxRDoKYev2l5KRZyEpIhBLbSPZpdUMiA5h9si4Tpn9qqysxGQynX/nmImIiIiISPcU4BtA2tCrmDVkDvvN+1n1xUts2PYh9qICcDg5aILQDz6B9z6BkSNbujn+7GfHXeZ4tI4afLRd8vj59yXkV9aRW16HKciPyOAaGpqa2ZpbQWyosdPCWmfRjNlJaMZM3EW/7RN3Ua2Ju6jWxF1Ua92H1Wbl84z3WfXZX5i4Lpubv7K2e/2jMcEkzbiOlLsex5CUdMafU2CpI313kWvGzBTkS155PfmWWvYWWvH1NpAQHsDYpIjTCmhdOWOmYHYSCmbiLvqhIu6iWhN3Ua2Ju6jWuh+n00ljfQ3+Kz9u6eb47bdYjHDzXGg2QFwNpEWMZ8bPHyPkklmnvczxaK3LHltnzA6UVJNfUUdMqJEZQ2MotjYQ4OsNOKlvamb2iN4dNiFRMPMgBTNxF/1QEXdRrYm7qNbEXVRrPcCWLax4/WFer9kAjh/jia8DpjTGMfuyexh0039gCDr2QOgzsS23gvTviogNNVJsrWf9AXO77DdlYBRD40I5+owz7TETEREREZGea9w45oxZS8zuVaR/9Dy7cjeDzUaTF3xhLOKLDb+l36dPkTZkDtNuewpj/8Fn9XFt2/Jvy60ADO1mzGJDja4zzsBA69lpdTXVZ/mFHp+CmYiIiIiIeJyPlw8TR81h4qg5FJbnsOr9Z/l854fUWssB+CHAxot5y/ny7uU8F3IN3H8/TJ161sscOzo7rcDS0jAEnIDTdXZaU13tWX3WiSiYiYiIiIjIOSU+oi+33fUyN9qXsuGzV0n/9EWyyvaDw8m0HCD7Q/jwQxgxAh54APtP5+MT3HlLC9uecdb27LS6mmpWdtqntKc9ZiehPWbiLlofL+6iWhN3Ua2Ju6jWzg/ZmZv49J2nueXVDIwFxa7ns8Lhicv9uLzvDGbd9CTRQ1K7bAxducdMlSsiIiIiIue8AYMncM9jn2A8mAdvvw0TJgCQPhCqDI28n5vObU+O4cm7h7H1X3/D4Wj28IhPj4KZiIiIiIh0H35+cP318M03ODdvxjl2DN607DNzAlur9vHkO3dz+y1RvP/nO6myFHl2vKdIwUxERERERLolw7hx/GLpVv7vuX3cOGQ+Uc4A12uljRb+/u3LLHogid/9Zhq5ezZ6cKQnp2AmIiIiIiLdmqnPYOY/+i6vLqvgt5f9N6neCbT2arQ3N7E+5ysqL78Yrr4a1q2Dc7DNhoKZiIiIiIj0CF7+Rsbd/F88/mY+r9y7mutMkwht8iK+GlKKnLByJVxyCYwcSeZfnuRg4R5PD9lF7fJFRERERKTHiZk0k4WTZvKzokJKX/0Thox/QNGR/WZ79vB/K/awd/NTDE5MIe2KXzBl3Dz8vP08Nl7NmImIiIiISI/lGxdP/G//F3Jz4Z//hIkTORQGe6OApiYyf9jGkhd+zsJf9uO1tx/msLXQI+NUMBMRERERkZ7Pzw9++lP4+mui12zk3tBL6Ws9EoecUFNayMpPnufOh4fy299fwTcH1tLsxpb7WsooIiIiIiLnFeP4Scwa/zkzS0rIfPkZ0r9exsZeVpq8gOpqdmaks3P3p0QmDuavN3+Asf/gLh+TZsxEREREROS8ZIiJYchv/8Tij80su+p1bqkfTFzNkReb7CR9vRfjoGEwdy588UWXdnNUMBMRERERkfObry+hP7uZq1fs56VHt/Jk8JVcVOTNFQcAhwM++gguvRQmTuiyIWgpo4iIiIiIyBGGMWO4cMzHXFhaCq+8An/5Cxw+3PLi/swu+1zNmImIiIiIiBwtOhp+85uWbo7vvAOTJnXpxymYiYiIiIiIHI+vLyxYABs3tuwz6yIKZiIiIiIiIqfiwgu77NYKZiIiIiIiIh6mYCYiIiIiIuJhCmYiIiIiIiIepnb5J+E8coic1WrFy0s5VrqOw+Gguroao9GoWpMupVoTd1Gtibuo1sRdrFYr8GNG6EwKZidRXl4OQFJSkodHIiIiIiIi54Ly8nLCwsI69Z4KZicRHh4OwKFDhzr9D7+rjR07lq1bt3bLzzube53ue0/n+lO59mTXHO91q9VKYmIi+fn5hIaGntJ4zhWqtc6/XrXWMdVa51+vWuuYaq3zr1etdUy11vnXd2WtVVVV0adPH1dG6EwKZifROh0eFhbW7f5D9/b2duuYO/PzzuZep/ve07n+VK492TUnez00NFS15sbPU62p1tz1eao11Zq7Pk+1plpz1+edz7XWFUtmtQi3B7v33nu77eedzb1O972nc/2pXHuya9z9/4s7qNY6/3rVWsdUa51/vWqtY6q1zr9etdYx1VrnX99da83g7Iqdaz2I1WolLCyMqqqqbvcbGOleVGviLqo1cRfVmriLak3cpStrTTNmJ+Hv789jjz2Gv7+/p4ciPZxqTdxFtSbuoloTd1Gtibt0Za1pxkxERERERMTDNGMmIiIiIiLiYQpmIiIiIiIiHqZgJiIiIiIi4mEKZiIiIiIiIh6mYCYiIiIiIuJhCmad6Oqrr8ZkMnHdddd5eijSw3zyyScMHjyYgQMH8uqrr3p6ONKD6fuYuEN+fj7Tpk1j2LBhjBw5kvfff9/TQ5IeqrKykjFjxjBq1CiGDx/OK6+84ukhSQ9XV1dHUlISDz300Gm/V+3yO9GXX35JdXU1b7zxBsuXL/f0cKSHsNvtDBs2jHXr1hEWFkZqairffPMNERERnh6a9ED6PibuUFRURElJCaNGjaK4uJjU1FQOHDhAUFCQp4cmPUxzczM2m43AwEBqa2sZPnw427Zt089Q6TK/+c1vyM7OJjExkeeff/603qsZs040bdo0QkJCPD0M6WG2bNnCBRdcQHx8PMHBwaSlpfHpp596eljSQ+n7mLhDXFwco0aNAiA2NpbIyEgqKio8Oyjpkby9vQkMDATAZrPhdDrRnIR0laysLPbv309aWtoZvf+8CWbr169nzpw59O7dG4PBwMqVK4+55sUXXyQ5ORmj0cj48ePZsmWL+wcqPc7Z1t7hw4eJj493PY6Pj6ewsNAdQ5duRt/nxF06s9YyMjJobm4mMTGxi0ct3VFn1FplZSUpKSkkJCTw8MMPExkZ6abRS3fSGbX20EMP8eyzz57xGM6bYFZbW0tKSgovvvhih6+/++67LF68mMcee4zt27eTkpLCzJkzKS0tdV3Tuj756H8OHz7sri9DuqHOqD2RU6FaE3fprFqrqKjgpptu4uWXX3bHsKUb6oxa69WrF7t27SInJ4e3336bkpISdw1fupGzrbWPPvqIQYMGMWjQoDMfhPM8BDhXrFjR7rlx48Y57733Xtfj5uZmZ+/evZ3PPvvsad173bp1zmuvvbYzhik90JnU3tdff+2cO3eu6/UHH3zQ+dZbb7llvNJ9nc33OX0fk9NxprXW0NDgnDJlivPvf/+7u4Yq3Vxn/P3t7rvvdr7//vtdOUzpAc6k1n71q185ExISnElJSc6IiAhnaGio84knnjitzz1vZsxOpLGxkYyMDGbMmOF6zsvLixkzZrBp0yYPjkx6ulOpvXHjxrFnzx4KCwupqalh1apVzJw501NDlm5K3+fEXU6l1pxOJ4sWLeKSSy7hxhtv9NRQpZs7lVorKSmhuroagKqqKtavX8/gwYM9Ml7pvk6l1p599lny8/PJzc3l+eef5/bbb+fRRx89rc/x6dRRd1Nms5nm5mZiYmLaPR8TE8P+/ftP+T4zZsxg165d1NbWkpCQwPvvv8+ECRM6e7jSg5xK7fn4+PD73/+e6dOn43A4+M///E91k5LTdqrf5/R9TM7WqdTa119/zbvvvsvIkSNd+zjefPNNRowY4e7hSjd2KrWWl5fHHXfc4Wr6cf/996vO5LR1VlY4GQWzTvT55597egjSQ1111VVcddVVnh6GnAf0fUzcYfLkyTgcDk8PQ84D48aNY+fOnZ4ehpxnFi1adEbv01JGIDIyEm9v72M2g5aUlBAbG+uhUcn5QLUn7qJaE3dRrYm7qNbEXdxVawpmgJ+fH6mpqaxdu9b1nMPhYO3atVrCI11KtSfuoloTd1Gtibuo1sRd3FVr581SxpqaGrKzs12Pc3Jy2LlzJ+Hh4fTp04fFixezcOFCxowZw7hx41iyZAm1tbXcfPPNHhy19ASqPXEX1Zq4i2pN3EW1Ju5yTtTa2TWT7D7WrVvnBI75Z+HCha5rli5d6uzTp4/Tz8/POW7cOOe3337ruQFLj6HaE3dRrYm7qNbEXVRr4i7nQq0ZnE6ns/NinoiIiIiIiJwu7TETERERERHxMAUzERERERERD1MwExERERER8TAFMxEREREREQ9TMBMREREREfEwBTMREREREREPUzATERERERHxMAUzERERERERD1MwExERERER8TAFMxEREREREQ9TMBMREREREfEwBTMREREREREP+/9RDDux+nFVxAAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 1000x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fitting results:\n",
      "gamma = 1.0307 ± 0.0028\n",
      "beta = 1.5659 ± 0.0034\n",
      "Input: a = 0.4, b = 0.7\n",
      "Theoretical beta for 2D Cauchy projection: 1.5\n",
      "Deviation from theory: 0.0659\n",
      "Points used: 999927\n",
      "CPU times: user 10.3 s, sys: 390 ms, total: 10.7 s\n",
      "Wall time: 11.1 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "import warnings; warnings.filterwarnings(\"ignore\", category=UserWarning); import matplotlib.pyplot as plt; rmax = clip\n",
    "u = np.random.uniform(0, 1, n); theta = np.arccos(1 - u); phi = 2 * np.pi * np.random.uniform(0, 1, n); X = a + b * np.sin(theta) * np.cos(phi) / np.cos(theta); Y = a + b * np.sin(theta) * np.sin(phi) / np.cos(theta)\n",
    "R = np.sqrt(X**2 + Y**2); R_clip = R[R < rmax]; bins = np.logspace(-2, np.log10(rmax), 2000); centers = (bins[:-1] + bins[1:])/2; counts, _ = np.histogram(R_clip, bins)\n",
    "density = counts / (2*np.pi*centers*np.diff(bins)); mask_nonzero = (centers > 0) & (density > 0); centers_clean = centers[mask_nonzero]; density_clean = density[mask_nonzero]\n",
    "def moffat_torch(r, A, gamma, beta): return A / (1 + (r/gamma)**2)**beta\n",
    "def fit_moffat(r_data, density_data, n_steps=steps*5):\n",
    "    r_tensor = torch.tensor(r_data, device=device, dtype=torch.float32); density_tensor = torch.tensor(density_data, device=device, dtype=torch.float32)\n",
    "    log_A = torch.nn.Parameter(torch.tensor(np.log(density_data.max()), device=device)); log_gamma = torch.nn.Parameter(torch.tensor(np.log(b), device=device)); log_beta = torch.nn.Parameter(torch.tensor(np.log(3.0), device=device))\n",
    "    opt = torch.optim.Adam([log_A, log_gamma, log_beta], lr=lr*2)\n",
    "    for _ in range(n_steps):\n",
    "        opt.zero_grad(); A = log_A.exp(); gamma = log_gamma.exp(); beta = log_beta.exp()\n",
    "        pred = moffat_torch(r_tensor, A, gamma, beta); loss = ((torch.log(pred) - torch.log(density_tensor))**2).mean(); loss.backward(); opt.step()\n",
    "    return log_A.exp().item(), log_gamma.exp().item(), log_beta.exp().item()\n",
    "mask = (centers_clean > 1) & (centers_clean < rmax/10) & (density_clean > density_clean.max()/1e6); A_est, gamma_est, beta_est = fit_moffat(centers_clean[mask], density_clean[mask])\n",
    "boots_params = []\n",
    "for i in tqdm(range(n_boot)):\n",
    "    idx = np.random.choice(len(R_clip), len(R_clip), replace=True); R_boot = R_clip[idx]\n",
    "    counts_boot, _ = np.histogram(R_boot, bins); density_boot = counts_boot / (2*np.pi*centers*np.diff(bins))\n",
    "    mask_boot = (centers > 0) & (density_boot > 0); centers_boot = centers[mask_boot]; density_boot = density_boot[mask_boot]\n",
    "    mask2 = (centers_boot > 1) & (centers_boot < rmax/10) & (density_boot > density_boot.max()/1e6)\n",
    "    if mask2.sum() > 10:\n",
    "        try: boots_params.append(fit_moffat(centers_boot[mask2], density_boot[mask2], n_steps=steps))\n",
    "        except: pass\n",
    "boots_params = np.array(boots_params); A_std = boots_params[:, 0].std(); gamma_std = boots_params[:, 1].std(); beta_std = boots_params[:, 2].std()\n",
    "plt.figure(figsize=(10, 4)); plt.loglog(centers_clean, density_clean, '.', ms=2, alpha=0.3, label='Data')\n",
    "r_fit = np.logspace(-1, np.log10(rmax), 2000); density_fit = moffat_torch(r_fit, A_est, gamma_est, beta_est)\n",
    "plt.loglog(r_fit, density_fit, 'r-', lw=2, label=f'Moffat fit: $\\\\beta$={beta_est:.3f}$\\\\pm${beta_std:.3f}')\n",
    "theoretical_beta = 1.5; density_theoretical = A_est * (1 + (r_fit/b)**2)**(-theoretical_beta)\n",
    "plt.loglog(r_fit, density_theoretical, 'g--', lw=2, alpha=0.7, label=f'Theoretical ($\\\\beta$={theoretical_beta})')\n",
    "plt.ylabel('I(r)'); plt.grid(True, alpha=0.3); plt.xlim(0.1, rmax); plt.ylim(density_clean.min()/10, density_clean.max()*10); plt.legend()\n",
    "plt.title(f'Moffat profile: $\\\\beta$ = {beta_est:.4f} $\\\\pm$ {beta_std:.4f}, $\\\\gamma$ = {gamma_est:.3f} $\\\\pm$ {gamma_std:.3f}'); plt.show()\n",
    "print(f\"Fitting results:\"); print(f\"gamma = {gamma_est:.4f} ± {gamma_std:.4f}\"); print(f\"beta = {beta_est:.4f} ± {beta_std:.4f}\")\n",
    "print(f\"Input: a = {a}, b = {b}\"); print(f\"Theoretical beta for 2D Cauchy projection: 1.5\")\n",
    "print(f\"Deviation from theory: {abs(beta_est - 1.5):.4f}\"); print(f\"Points used: {len(R_clip)}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "741fbe0d-ab47-40a7-bc0b-2a53e0c78489",
   "metadata": {},
   "source": [
    "# Fact check on FTL data from Hubble"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "70a70264-f19e-4fc8-acd5-84cd7a01b28a",
   "metadata": {},
   "source": [
    "## Helpers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "68f61813-fa32-4682-921a-55ecb7c83af1",
   "metadata": {},
   "outputs": [],
   "source": [
    "def download_hubble_flt_data(region_dict):\n",
    "   target_name, filter_name, exposure_range = region_dict['name'], region_dict['filter'], region_dict['exposure']; index = region_dict.get('index', 0)\n",
    "   obs = Observations.query_criteria(obs_collection='HST', instrument_name='ACS/WFC', filters=filter_name, target_name=target_name, t_exptime=[exposure_range[0], exposure_range[1]])\n",
    "   if len(obs) == 0: raise ValueError(f\"No observations found for target {target_name} with exposure {exposure_range}\")\n",
    "   if index >= len(obs): print(f\"Warning: index {index} out of range, using index 0\"); index = 0\n",
    "   obs.sort('t_exptime'); selected_obs = obs[index]; products = Observations.get_product_list(selected_obs)\n",
    "   flt_products = Observations.filter_products(products, productSubGroupDescription='FLT', dataproduct_type='image')\n",
    "   if len(flt_products) == 0: raise ValueError(f\"No FLT products found for {target_name}\")\n",
    "   manifest = Observations.download_products(flt_products[0]); downloaded_file = manifest['Local Path'][0]\n",
    "   with fits.open(downloaded_file) as hdul: data = hdul[1].data.astype(float); wcs = WCS(hdul[1].header, hdul); return data, wcs, target_name"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "950d448e-12b0-42bf-a0c2-9c1c4dae9ab3",
   "metadata": {},
   "outputs": [],
   "source": [
    "def compute_radial_profile(cutout, x_center, y_center):\n",
    "   y, x = np.ogrid[:cutout.shape[0], :cutout.shape[1]]; r = np.sqrt((x - x_center)**2 + (y - y_center)**2)\n",
    "   r_int = r.astype(int); r_max = int(r.max()); radial_profile = []; radii = []\n",
    "   for radius in range(r_max + 1):\n",
    "       mask = (r_int == radius)\n",
    "       if mask.sum() > 0: radii.append(radius); radial_profile.append(np.mean(cutout[mask]))\n",
    "   return np.array(radii), np.array(radial_profile)\n",
    "\n",
    "def fit_moffat_star(data, x, y, size=10):\n",
    "   try:\n",
    "       x_int, y_int = int(x), int(y); x_min, x_max = max(0, x_int - size//2), min(data.shape[1], x_int + size//2); y_min, y_max = max(0, y_int - size//2), min(data.shape[0], y_int + size//2)\n",
    "       cutout = data[y_min:y_max, x_min:x_max].copy()\n",
    "       if cutout.shape[0] < 5 or cutout.shape[1] < 5 or not np.all(np.isfinite(cutout)): return None\n",
    "       mask = np.ones_like(cutout, dtype=bool); mask[1:-1, 1:-1] = False; background = np.median(cutout[mask]); cutout_nobg = cutout - background\n",
    "       y_grid, x_grid = np.mgrid[:cutout.shape[0], :cutout.shape[1]]; max_pos = np.unravel_index(np.argmax(cutout_nobg), cutout_nobg.shape)\n",
    "       radii, profile = compute_radial_profile(cutout_nobg, max_pos[1], max_pos[0])\n",
    "       max_radius = min(size//2, len(radii)); radii = radii[:max_radius]; profile = profile[:max_radius]\n",
    "       if len(radii) < 4: return None\n",
    "       moffat_init = models.Moffat1D(amplitude=np.max(profile), x_0=0.0, gamma=1.0, alpha=1.0); moffat_init.x_0.fixed = True\n",
    "       fit_p = fitting.LevMarLSQFitter()\n",
    "       try: moffat_fit = fit_p(moffat_init, radii, profile)\n",
    "       except: return None\n",
    "       residual = profile - moffat_fit(radii); residual_std = np.std(residual)\n",
    "       if residual_std > 0: chi2 = np.sum((residual**2) / (residual_std**2)); dof = len(radii) - 2; p_value = 1.0 - stats.chi2.cdf(chi2, dof) if dof > 0 and chi2 > 0 else 0\n",
    "       else: return None\n",
    "       fwhm = 2 * moffat_fit.gamma.value * np.sqrt(2**(1/moffat_fit.alpha.value) - 1)\n",
    "       return {'alpha': moffat_fit.alpha.value, 'gamma': moffat_fit.gamma.value, 'p_value': p_value, 'fwhm': fwhm}\n",
    "   except Exception as e: return None"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "58658783-0391-42fa-93e3-d8373ced6a4c",
   "metadata": {},
   "outputs": [],
   "source": [
    "def create_histograms(alpha_values, gamma_values, fwhm_values, target_name):\n",
    "    import matplotlib.pyplot as plt; import scienceplots; from scipy.optimize import curve_fit\n",
    "    plt.style.use(['science', 'ieee']); fig, axes = plt.subplots(1, 3, figsize=(15, 2))\n",
    "    fig.text(0.04, 0.5, target_name, fontsize=14, rotation=90, verticalalignment='center', horizontalalignment='center')\n",
    "    def power_law(x, A, alpha): return A * x**(-alpha)\n",
    "    counts_alpha, bins_alpha = np.histogram(alpha_values, bins=200); frequencies_alpha = counts_alpha / len(alpha_values)\n",
    "    bin_centers_alpha = (bins_alpha[:-1] + bins_alpha[1:]) / 2; mask_alpha = (bin_centers_alpha >= 0.5) & (bin_centers_alpha <= 8)\n",
    "    tail_mask_alpha = alpha_values > 1.5; tail_values_alpha = alpha_values[tail_mask_alpha]\n",
    "    if len(tail_values_alpha) > 10:\n",
    "        try:\n",
    "            hist_tail, bins_tail = np.histogram(tail_values_alpha, bins=50, range=(1.5, 20)); centers_tail = (bins_tail[:-1] + bins_tail[1:]) / 2\n",
    "            hist_tail = hist_tail / (len(alpha_values) * np.diff(bins_tail)); mask_fit = (hist_tail > 0) & (centers_tail > 2.0)\n",
    "            popt_alpha, pcov_alpha = curve_fit(power_law, centers_tail[mask_fit], hist_tail[mask_fit], p0=[0.1, 2.0])\n",
    "            std_alpha = np.sqrt(np.diag(pcov_alpha)); tail_text_alpha = r'Tail: $\\alpha$=' + f'{popt_alpha[1]:.2f}' + r'$\\pm$' + f'{std_alpha[1]:.2f}'\n",
    "        except: tail_text_alpha = 'Tail fit failed'\n",
    "    else: tail_text_alpha = 'Insufficient tail data'\n",
    "    axes[0].bar(bin_centers_alpha[mask_alpha], frequencies_alpha[mask_alpha], width=bins_alpha[1]-bins_alpha[0], alpha=0.4, edgecolor='black')\n",
    "    axes[0].axvline(x=np.median(alpha_values), color='red', linestyle='--', linewidth=2, label=f'Median: {np.median(alpha_values):.2f}')\n",
    "    axes[0].axvline(x=1.5, color='black', linestyle='--', linewidth=2, alpha=0.7, label=r'$\\beta=1.5$')\n",
    "    axes[0].text(0.95, 0.95, tail_text_alpha, transform=axes[0].transAxes, fontsize=9, verticalalignment='top', horizontalalignment='right', bbox=dict(boxstyle='round', facecolor='wheat', alpha=0.5))\n",
    "    axes[0].set_xlabel(r'Alpha ($\\beta$)'); axes[0].set_ylabel('Frequency'); axes[0].set_title(r'Alpha ($\\beta$) Distribution')\n",
    "    axes[0].set_xlim(0.5, 8); axes[0].legend(); axes[0].grid(True, alpha=0.3)\n",
    "    counts_gamma, bins_gamma = np.histogram(gamma_values, bins=200); frequencies_gamma = counts_gamma / len(gamma_values)\n",
    "    bin_centers_gamma = (bins_gamma[:-1] + bins_gamma[1:]) / 2; mask_gamma = (bin_centers_gamma >= 0.25) & (bin_centers_gamma <= 2.5)\n",
    "    tail_mask_gamma = gamma_values > 1.0; tail_values_gamma = gamma_values[tail_mask_gamma]\n",
    "    if len(tail_values_gamma) > 10:\n",
    "        try:\n",
    "            hist_tail, bins_tail = np.histogram(tail_values_gamma, bins=50, range=(1.0, 10)); centers_tail = (bins_tail[:-1] + bins_tail[1:]) / 2\n",
    "            hist_tail = hist_tail / (len(gamma_values) * np.diff(bins_tail)); mask_fit = (hist_tail > 0) & (centers_tail > 1.2)\n",
    "            popt_gamma, pcov_gamma = curve_fit(power_law, centers_tail[mask_fit], hist_tail[mask_fit], p0=[0.1, 2.0])\n",
    "            std_gamma = np.sqrt(np.diag(pcov_gamma)); tail_text_gamma = r'Tail: $\\alpha$=' + f'{popt_gamma[1]:.2f}' + r'$\\pm$' + f'{std_gamma[1]:.2f}'\n",
    "        except: tail_text_gamma = 'Tail fit failed'\n",
    "    else: tail_text_gamma = 'Insufficient tail data'\n",
    "    axes[1].bar(bin_centers_gamma[mask_gamma], frequencies_gamma[mask_gamma], width=bins_gamma[1]-bins_gamma[0], alpha=0.4, edgecolor='black', color='orange')\n",
    "    axes[1].axvline(x=np.median(gamma_values), color='red', linestyle='--', linewidth=2, label=f'Median: {np.median(gamma_values):.2f}')\n",
    "    axes[1].axvline(x=1.0, color='blue', linestyle='--', linewidth=2, alpha=0.7, label=r'$\\gamma=1.0$')\n",
    "    axes[1].text(0.95, 0.95, tail_text_gamma, transform=axes[1].transAxes, fontsize=9, verticalalignment='top', horizontalalignment='right', bbox=dict(boxstyle='round', facecolor='wheat', alpha=0.5))\n",
    "    axes[1].set_xlabel(r'Gamma ($\\gamma$)'); axes[1].set_ylabel('Frequency'); axes[1].set_title(r'Gamma ($\\gamma$) Distribution')\n",
    "    axes[1].set_xlim(0.25, 2.5); axes[1].legend(); axes[1].grid(True, alpha=0.3)\n",
    "    counts_fwhm, bins_fwhm = np.histogram(fwhm_values, bins=200); frequencies_fwhm = counts_fwhm / len(fwhm_values)\n",
    "    bin_centers_fwhm = (bins_fwhm[:-1] + bins_fwhm[1:]) / 2; mask_fwhm = (bin_centers_fwhm >= 0.5) & (bin_centers_fwhm <= 2.5)\n",
    "    tail_mask_fwhm = fwhm_values > np.sqrt(2); tail_values_fwhm = fwhm_values[tail_mask_fwhm]\n",
    "    if len(tail_values_fwhm) > 10:\n",
    "        try:\n",
    "            hist_tail, bins_tail = np.histogram(tail_values_fwhm, bins=50, range=(np.sqrt(2), 10)); centers_tail = (bins_tail[:-1] + bins_tail[1:]) / 2\n",
    "            hist_tail = hist_tail / (len(fwhm_values) * np.diff(bins_tail)); mask_fit = (hist_tail > 0) & (centers_tail > 1.6)\n",
    "            popt_fwhm, pcov_fwhm = curve_fit(power_law, centers_tail[mask_fit], hist_tail[mask_fit], p0=[0.1, 2.0])\n",
    "            std_fwhm = np.sqrt(np.diag(pcov_fwhm)); tail_text_fwhm = r'Tail: $\\alpha$=' + f'{popt_fwhm[1]:.2f}' + r'$\\pm$' + f'{std_fwhm[1]:.2f}'\n",
    "        except: tail_text_fwhm = 'Tail fit failed'\n",
    "    else: tail_text_fwhm = 'Insufficient tail data'\n",
    "    axes[2].bar(bin_centers_fwhm[mask_fwhm], frequencies_fwhm[mask_fwhm], width=bins_fwhm[1]-bins_fwhm[0], alpha=0.4, edgecolor='black', color='green')\n",
    "    axes[2].axvline(x=np.median(fwhm_values), color='red', linestyle='--', linewidth=2, label=f'Median: {np.median(fwhm_values):.2f}')\n",
    "    axes[2].axvline(x=np.sqrt(2), color='purple', linestyle='--', linewidth=2, alpha=0.7, label=r'$\\sqrt{2}$')\n",
    "    axes[2].text(0.95, 0.95, tail_text_fwhm, transform=axes[2].transAxes, fontsize=9, verticalalignment='top', horizontalalignment='right', bbox=dict(boxstyle='round', facecolor='wheat', alpha=0.5))\n",
    "    axes[2].set_xlabel('FWHM (pixels)'); axes[2].set_ylabel('Frequency'); axes[2].set_title('FWHM Distribution')\n",
    "    axes[2].set_xlim(0.5, 2.5); axes[2].legend(); axes[2].grid(True, alpha=0.3)\n",
    "    plt.tight_layout(); plt.subplots_adjust(left=0.1)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "413633d9-0e03-4f80-b19e-6f84dde6b654",
   "metadata": {},
   "outputs": [],
   "source": [
    "def analyze_hubble_field(data, target_name):\n",
    "   mean, median, std = sigma_clipped_stats(data, sigma=3.0)\n",
    "   threshold = 5.0 * std; daofind = DAOStarFinder(threshold=threshold, fwhm=1.0, sharplo=0.0, sharphi=3.0, roundlo=-1.0, roundhi=1.0)\n",
    "   sources = daofind(data - median)\n",
    "   if sources is None or len(sources) == 0: return None\n",
    "   positions = np.transpose((sources['xcentroid'], sources['ycentroid'])); fluxes = sources['flux']\n",
    "   edge_distance = 10; candidates = []\n",
    "   for i, (x, y) in enumerate(positions):\n",
    "       if (x < edge_distance or x > data.shape[1] - edge_distance or y < edge_distance or y > data.shape[0] - edge_distance): continue\n",
    "       candidates.append((i, x, y, fluxes[i]))\n",
    "   candidates.sort(key=lambda x: x[3], reverse=True); results = []\n",
    "   for idx, (_, x, y, _) in enumerate(tqdm(candidates, desc=\"Fitting stars\")):\n",
    "       result = fit_moffat_star(data, x, y, size=10)\n",
    "       if result is not None: results.append(result)\n",
    "   alpha_values = np.array([r['alpha'] for r in results]); gamma_values = np.array([r['gamma'] for r in results])\n",
    "   p_values = np.array([r['p_value'] for r in results]); fwhm_values = np.array([r['fwhm'] for r in results])\n",
    "   mask_nonzero = p_values > 0; valid_alpha = alpha_values[mask_nonzero]; valid_gamma = gamma_values[mask_nonzero]; valid_fwhm = fwhm_values[mask_nonzero]\n",
    "   if len(valid_alpha) < 50: return None\n",
    "   mask_reasonable = (valid_alpha > 0.5) & (valid_alpha < 10) & (valid_gamma > 0.1) & (valid_gamma < 10)\n",
    "   valid_alpha = valid_alpha[mask_reasonable]; valid_gamma = valid_gamma[mask_reasonable]; valid_fwhm = valid_fwhm[mask_reasonable]\n",
    "   if len(valid_alpha) < 50: return None\n",
    "   percentile_low = 0.5; percentile_high = 99.5\n",
    "   alpha_min = np.percentile(valid_alpha, percentile_low); alpha_max = np.percentile(valid_alpha, percentile_high)\n",
    "   gamma_min = np.percentile(valid_gamma, percentile_low); gamma_max = np.percentile(valid_gamma, percentile_high)\n",
    "   mask_filtered = (valid_alpha >= alpha_min) & (valid_alpha <= alpha_max) & (valid_gamma >= gamma_min) & (valid_gamma <= gamma_max)\n",
    "   final_alpha = valid_alpha[mask_filtered]; final_gamma = valid_gamma[mask_filtered]; final_fwhm = valid_fwhm[mask_filtered]\n",
    "   create_histograms(final_alpha, final_gamma, final_fwhm, target_name)\n",
    "   return {'alpha_values': final_alpha, 'gamma_values': final_gamma, 'fwhm_values': final_fwhm, 'star_count': len(final_alpha)}"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c3c96337-1510-4e65-813d-c84bdc0aaef2",
   "metadata": {},
   "source": [
    "## Check!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "553c4627-58f0-4968-b3a4-c0075ad09758",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "4013dd2ed3d745c4a4cdb3f2c522ac72",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Processing regions:   0%|          | 0/20 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "6f4a515c9755482ba342471714ab4b2c",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Fitting stars:   0%|          | 0/10789 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 9000x1200 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "3e9ce8a1da6047a9bcd385289f657c28",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Fitting stars:   0%|          | 0/1587 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
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      "text/plain": [
       "<Figure size 9000x1200 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "423ee74f3b374af8a5a925ff644e3e61",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Fitting stars:   0%|          | 0/5808 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
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      "text/plain": [
       "<Figure size 9000x1200 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "fa5d6a9459b64e3e912803466c7eda8c",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Fitting stars:   0%|          | 0/5845 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
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      "text/plain": [
       "<Figure size 9000x1200 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "3860f569fcbb490d9dee4053e19fd442",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Fitting stars:   0%|          | 0/2524 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
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      "text/plain": [
       "<Figure size 9000x1200 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "eebaa507e9ad4abf8b4c5c97bca5f340",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Fitting stars:   0%|          | 0/1901 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
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      "text/plain": [
       "<Figure size 9000x1200 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "725f50c144c04cd5a11c51b9fc45ee7c",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Fitting stars:   0%|          | 0/55935 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
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      "text/plain": [
       "<Figure size 9000x1200 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "3c10783acc804fd886fe6d72ec4d2040",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Fitting stars:   0%|          | 0/33058 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
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      "text/plain": [
       "<Figure size 9000x1200 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "bc40fee1fdf24916b5645c82c5216f63",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Fitting stars:   0%|          | 0/38225 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
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      "text/plain": [
       "<Figure size 9000x1200 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "eccf206f16f14d5499596df0f315395c",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Fitting stars:   0%|          | 0/25163 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
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      "text/plain": [
       "<Figure size 9000x1200 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
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       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Fitting stars:   0%|          | 0/43238 [00:00<?, ?it/s]"
      ]
     },
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      "text/plain": [
       "<Figure size 9000x1200 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Fitting stars:   0%|          | 0/24157 [00:00<?, ?it/s]"
      ]
     },
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     "output_type": "display_data"
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      "text/plain": [
       "<Figure size 9000x1200 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
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       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Fitting stars:   0%|          | 0/14822 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
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      "text/plain": [
       "<Figure size 9000x1200 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
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       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Fitting stars:   0%|          | 0/10323 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
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      "text/plain": [
       "<Figure size 9000x1200 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "332dd00b4c6b4501ad928dc319aa5fea",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Fitting stars:   0%|          | 0/10817 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
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      "text/plain": [
       "<Figure size 9000x1200 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "3c725506d9194fefaca53b7132fcfa9e",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Fitting stars:   0%|          | 0/6092 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
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VRG0Lii/PuUttCwgh3vOvZcUwFoohBtgGRcpfsbbFmAzSF2t/T4ta2Hrdu/AriQAAsPUmf1AkhLi+gARYh/F4HHZ2dkIIr3LeycnJQhMbBoNB2N/fn/n34+PjUKvVVg0TYK0uJ2UtW7ze3d0No9Fo6vmTkxNf6AFb4TKPViqVUK1Wb0x0DcEPbQL5dn1SSafTCc1mM+OIALKTNJkshBCazWbodDoZRASwPtcnvy57EWeSye+kz8/PV7rgFGCdki4EWDZvTV4gbz4OsAnXb/hxaZk8ltZ6lhHrvB51U4qqCHkjSVZ9tqj7E67L+3Eecw3MeIOiy8v1SzHkuRhigBjEnjfUMCAuseeMJOoXkK2Y84b6BWQr1rH+KmL4/I8hBliXIuWNWNtiDEKRxNrP0qLeAcSiqHlBnoViy3tfU9sGYv7+7boY8m0MMQBfiz1/xVpTNMaCbMWeu5KobQEx5y61LSCEeM+/VhHDWCiGGKDoipS/Ym2LMRmkL9b+nha1sPUrZR0AAACQvZhOUgA2pdvtXv3/+Ph44VxYq9Vu/eHNXq+3bGgAGzEej0O/3w/1ej202+2l1nF4eJj4/Gg0WiU0gFzo9/tXP6rZ6/XC/fv3M44IIF0PHz4MIbyqHZrkBWyzbrcbWq3W1PP1ev3W+iBAXl2OAzudTmoXhw4GgxuPa7Wa76iBqD169GjquWXzVqVSufHYdyjAuvX7/akLmZYdf7377rtTz12OF9ct1nk96qYUUVHyRpIs+myR9ydcKsJxHnMNzHiDostDbTiGPBdDDBCL2POGGgbEJfackUT9ArIVc95Qv4BsxTrWX1YMn/8xxADrVKS8EWtbjEEoklj7WVrUO4AYFDkvyLNQXEXoa2rbQMzfv12KId/GEANwU+z5K9aaojEWZCv23JVEbQuIOXepbQEhxHv+tawYxkIxxADboEj5K9a2GJNB+mLt72lRC1u/UtYBAAAA2fMDwsA2uiyKdTqdqR9Emlez2QzVajXxbx9++OHSsQFswsOHD0O5XA4ffPDB0utIa4IYQN6Mx+Pw/vvvhxBCaLfbM8eEAHl1feLE4eFhtsEAZKjf74dWqzX1fLVazXxiHcA6jEajMBwOQ71eT3XS7uRE5Uajkdq6AdZhNBpNPTccDpda15tvvjn13OTFCgBpSrpoadnxV9JyR0dHG8ljMc7rUTelqIqSNyZl1WeLuj/hurwf5zHXwIw32AZ5uH4phjwXQwwQi9jzhhoGxCX2nDFJ/QKyF2veUL+A7MU41l9FDJ//McQA61SkvBFjW4xBKJoY+1la1DuAWBQ1L8izUGx572tq20AI8X7/dl0M+TaGGICbYs9fMdYUjbEge7HnrklqW0AI8eYutS3gUoznX6uIYSwUQwywDYqUv2JsizEZrEeM/T0tamGbUco6AAAAAIBNGw6HYTQahUqlsvIEh1mFq5gKQABJ+v1++OCDD0K5XF5pPUnLL/uFBUBeNBqNMB6PQ7VaNQECKKTLiRPlcjnVCwMA8mQ4HCZO/iqXy+Gjjz7KICKA9et0OqFcLocPPvgg1fUOBoMbj999991U1w+QtqTvekej0VLrOj09nXpu1e9mAGYZDodhOBxOPV+r1ZZa36zlut3uUuubV6zzetRNKaKi5I0kWfTZIu9PuFSE4zzmGpjxBmQvhjwXQwzAfNQwgFWpXwCzqF9AtmId6y8rhs//GGKAdSpS3oi1LcYgFEms/Swt6h1ADIqcF+RZKK4i9DW1bSAPYsi3McQA5EusNUVjLGBRaltAzNS2gBDiPf9aVgxjoRhigG1QpPwVa1uMySB9sfb3tKiFbUYp6wAAAAAANu1yIkIaP6R+W+Eoy+IawF1OT09DvV5fy7orlcpa1gsQg263ezWe7PV6GUcDkL7BYHA1ceLBgwcZRwOQjfF4HBqNRuLfDg8P/Zg6UFiHh4fh5OQk1Tw3GAxufF9SrVblUSB6SXnq0aNHS61rNBrdeOw7FGCdLi/EmrRK7kladtmcOK8Y5/Wom1JURckbk7Lqs0Xdn3BdEY7zWGtgxhsQhxjyXAwxAPNRwwBWoX4B3Eb9ArIV41h/FTF8/scQA6xTkfJGjG0xBqFoYuxnaVHvAGJR1Lwgz0KxFaGvqW0DeRBDvo0hBiBfYqwpGmMBi1LbAmKntgWEEOf51ypiGAvFEANsgyLlrxjbYkwG6xFjf0+LWtjmlLIOAAAAAGDTHj16FMrlcqjX66msb1ZxzY/LAdtg8kuEer0u/wGFNRqNQqvVCiGE0Ol0/JAmUEjXJ6EcHByE3d3d0Gg0QrfbvZrIAVB077///tSPqIfw6qKmZrOZQUQAm5P2uW6v17vx+PK8GiBmSbmw3+8njhHv8vjx4xuPq9Xq0nEB3OXyQrPrVs07ScsPh8O1XmwW47wedVOKqih5Y1JWfbao+xOuK8pxHmMNzHgD4hBDnoshBmA+ahjAKtQvgLuoX0B2YhzrryKGz/8YYoB1KlLeiLEtxiAUTYz9LC3qHUAsipoX5FkotqL0NbVtIHYx5NsYYgDyJcaaojEWsCi1LSAP1LaAGM+/VhHDWCiGGGAbFCl/xdgWYzJYjxj7e1rUwjanlHUAAAAAAJv24MGDqQkJq0gqoGVRVAPYtKSC/YMHDzKIBGAzGo1GCOHVF6t+lB0oouFwODVxYjQahX6/H1qtVtjb2ws7Ozuh0WiEfr+fUZQA6zUcDmfmuA8++GDD0QDk34cffnjj8bvvvptRJADzm3Wx/GV9cF7dbnfqooFlLpQHmMdoNEq8UOmtt95aab1vv/124vOT47w0xTavR92UoipS3rguqz5b1P0J1znOZ1u1Bma8AXGIIc/FEAMwPzUMYFnqF0AW1C9gfrGN9VcRw+d/DDHAuhUpb8TWFmMQiii2fpYW9Q4gFkXNC/IsFJu+NpvaNpCmGPJtDDEA+RNbTdEYC1iU2hawrdS2IH9iO/9aRQxjoRhigG1RpPwVW1uMyWB9YuvvaVEL26xS1gEAAAAAbFq9Xg+1Wi219d2/f3/quVk/2ARQJI8ePbrx+PDwMFSr1YyiAVivg4ODMBwOQ7lcTvVLWoCYPHz48M7XjMfj0O/3Q6PRCPfu3QuNRiOMRqMNRAewGe+//37i89Vq1TkvwIIGg8GNibnVajWTickAi3rvvfcSnx8Oh6HVas29nsPDwxuP0/6eGuC6yQuxLu3u7q603lnnwsfHxyut9zaxzetRN6WoipQ3rsuqzxZ1f8J1jvNkadTAjDcgDjHkuRhiAOanhgEsS/0C2DT1C1hMbGP9VcTw+R9DDLBuRcobsbXFGIQiiq2fpUW9A4hFUfOCPAvFpq8lU9sG0hZDvo0hBiB/YqspGmMBi1LbAraR2hbkU2znX6uIYSwUQwywLYqUv2JrizEZrE9s/T0tamGbVco6AAAAAIC8Ozs7m3oui8IawCaNx+PQ7XavHjebzdButzOMCGB9hsNhODo6CiGE8MEHH/ghYaCQLidiLKrf74fd3d3QarVuTP4HyKPBYBCGw2Hi3x48eLDhaADyr9fr3Xj83nvvZRQJwGKq1erMCzW63W5otVp3rqPVat24wKFSqYQPPvggtRgBJs26SGnV+StJF5uFEGaeP8dolXk96qYUWRHzRpZ9toj7EyY5zpOtWgMz3oB4xJDnYogByI4aBmwH9QsgC+oXkK0s70MQw+d/DDFA3hTp/iXqHbB+MeQM9Q4gJkXMC/IsFJ++lkxtG0hbDPk2hhgA1O6BTVLbAraV2hYQgvmjMcQALCeGOWlpUQuD7RFD7lIL27xS1gEAAAAA5N31H1W65AfmgKI7ODi4Ksi32+3Q6XSyDQhgjRqNRgghhHq9Hur1esbRAKzHw4cPV1q+2+2GP/zDPwyDwSCliAA27/DwcObfjAMBFvfhhx/eeCyXAnnS6XRCuVxO/Fu3272qGc76e7fbvXpcqVTCycnJzPUBpGHWRUqr5p5ZF1UlzZWJ1SrzetRNKbIi5o0s+2wR9ydMcpwnW7UGZrwB8Yghz8UQA5AdNQzYDuoXQBbULyBbWd6HIIbP/xhigLwp0v1L1Dtg/WLIGeodQEyKmBfkWSg+fS2Z2jaQthjybQwxAKjdA5uktgVsK7UtIATzR2OIAVhODHPS0qIWBtsjhtylFrZ5pawDAAAAAMi7pMJSrVbLIBKAzTg6Orr6Ubler3frjxcD5F2j0Qij0SiUy+XwwQcfZB0OwNrs7u6GWq0WqtXq0hMlxuNx2N/fv/EDxAB5MRqNZk46m6z19fv90Gg0ws7OTrh3797Vv93d3bC/vx+Ojo6imRwGkJXhcBjG4/HV40qlMnNCLUCMKpVK6PV6M//e7/fD7u7u1Ljv4OAgtFqtq8e1Wi2cnp6ufFECwF1mnYeuOga7LX/l5dx3lXk96qYUWRHzRpZ9toj7EyY5zqelUQMz3oB4xJDnYogByI4aBmwH9Qtg09QvIHtZ3ocghs//GGKAvCnS/UvUO2D9YsgZ6h1ATIqYF+RZKD59bZraNrAOMeTbGGIAULsHNkltC9hGalvAJfNHs48BWE4Mc9LSohYG2yOG3KUWtnmlrAMAAAAAyLOkolqz2fTjSkBhHRwchIODgxBCCPV6PbdfggLMo9/vh36/H0IIodfrGeMBhdZsNsPx8XE4OTkJ5+fn4eLiIpycnITDw8OFx3ytVusqfwLkxW15a39/P4QQQrfbDTs7O6HRaIR+v3/jwqcQXk0GGwwG4eDgIOzu7oZGoxHFBDGALHQ6nRuP6/V6RpEALK9Wq03ls+tGo1HY3d0N3W736iKGo6Ojq793Op1wfHy8iVCBLTd5fnrd/fv3V17/rO9HkubMxGbVeT3qphRVUfNGVn22qPsTrnOcJ0ujBma8AXGIIc/FEAOQHTUM2B7qF8CmqV9AtrK8D0EMn/8xxAB5U6T7l6h3wPrFkjPUO4BYFDUvyLNQbPpaMrVtIG0x5NsYYgBQuwc2TW0L2EZqW0AI5o/GEAOwnFjmpKVBLQy2Ryy5Sy1s80pZBwAAAACQZ48ePZp67uDgIINIANZrNBpN/ahcv98POzs78h5QSOPxOLz//vshhFdfYi76ZSVAEVSr1dBut8Px8XG4uLgIvV5v7nzYaDSimBQBMK+kOt91u7u7odVq3TrRbFK/3w+7u7smvwJb6cMPP7zx+L333ssoEoDVNJvNqYveJ7VarbCzsxMGg8HVMufn56HZbG4iRIBwdnY28295vKg1TeuY16NuShFsU97YRJ/dpv3J9nKcJ1tXDcx4AzYvhjwXQwxAdtQwYLupXwDrpH4B2cryPgQxfP7HEAPkTZHuX6LeAesXc85Q7wCysE15QZ6F4tDXkqltA2mLId/GEAOA2j0QA7UtoOjUtoAQzB+NIQZgOTHPSVuUWhhsj5hzl1rYepWyDgAAAAAgzyZ/WLPZbIZKpZJRNADpG4/HodVqhd3d3asflZt0dHQUdnZ2wmg02nB0AOvTaDTCeDwOlUrlzh/fBNgW9Xo9HB8fh9PT01Cv1+98/TvvvBPG4/H6AwNIwW2TzA4ODsJoNArNZjP0er1wcnISzs/Pw8XFRTg9PQ2dTufWCW2NRiMcHR2tI2yAKA2HwxvjwHK5HKrVanYBAazochw472s7nU7hL0IA4pLV97S3XYwVi03M61E3JY+2OW+so89u8/5kezjOp22yBma8AesXQ56LIQYgO2oYwHXqF0Ba1C8ge1nehyCGz/8YYoC8KdL9S9Q7YP3ylDPUO4BN2Oa8IM9Cfulr09S2gXWIId/GEAOA2j0QI7UtoEjUtoBL5o9mHwOwnDzNSbuLWhhsjzzlLrWwdJWyDgAAAAAgrwaDwY3CUrlcDoeHhxlGBJCewWAQGo1G2NnZCd1u987Xj8fjsLu7GwaDwQaiA1ivbrd7lc/m/dFNgG1SqVRCr9cLp6ent04uGY/H4eHDhxuMDGA5w+Hw1r83m81wfn4eOp1OqNfroVqtXv3YeqVSCc1mMxwfH4fj4+OZP8J+cHDgnBnYGo8ePbrxuNlsZhQJQHouL2K4S7fbDY1GYwMRAXxt3Rdb3r9/P5PtrmrT83rUTckTeSPdPmt/sg0c59OyqIEZb8D6xJDnYogByIYaBjCL+gWwKvULyFbW9yGI4fM/hhggT7LOG2lS74D1y2vOUO8A1klekGchj/S1aWrbwDrEkG9jiAHYbmr3QOzUtoAiUNsCQsh+TkcMY6EYYgAWl3X+SpNaGGyPvOYutbB0lLIOAAAAACCvJotoH3zwwcwf3wTIk729vbC/vx/6/f7Cy+7v79/40gEgb0ajUWi1WiGEV+O9arWacUQA8apUKuH09PTWCf9HR0dRTI4AuM3jx49n/q3dbodOpzNX3a9Wq4WTk5OZr200GnIisBW63e6Nx++9915GkQCk667x3qV+vx92d3d9XwJszNnZWSbb/fjjjzPZ7ryymtejbkoeyBtfS6PP2p9sA8f5tCxrYMYbkL4Y8lwMMQDZUMMA7qJ+ASxL/QKylfV9CGL4/I8hBsiTrPNGmtQ7YP3ynjPUO4B1kBe+Js9Cfuhr09S2gXWIId/GEAOw3dTugbxQ2wLyTG0LCCH7OR0xjIViiAFYXNb5K01qYbA98p671MJWU8o6AAAAAIA8Gg6HYTAYXD2u1+uhXq9nGBFAej766KNwfn4ezs/Pw+npaTg5OQm9Xi80m825vkDY399ff5AAa9JoNEIIIVSr1dButzOOBiAfOp3OrTlz8gIBgNicnp7O/Nvk5Lq7VCqV0Ov1Ev82Ho/lRKDwhsPhjQm75XI5VKvV7AICSNnjx4/nuqBpNBqFvb29MBwO1x8UsPXu37+/1vXn6SKzSzHM61E3JWbyxrRV+qz9yTZwnN8USw3MeAPSE0OeiyEGYPPUMIBFqF8Ai1C/gGzFMNaP4fM/hhggL2LIG2mJoS3GIBRdDP0sLeodQJrkhWnyLMRPX7tJbRtYlxjybQwxANsrhpqiMRawKLUtIG/UtoAQ4jj/imEsFEMMwGJiyF9piaEtxmSwGTH097SohS2nlHUAAAAAAHn0/vvvX/3/th/cBMijcrl89a9SqYRqtRrq9XrodDrh17/+9a3F+BBe/eBcv9/fULQA6Tk4OLj6sUzjO4DFHB4ehlqtlvi34+PjDUcDsJhZP64+K6/dpVarzZyE9/Dhw6XWCZAXjx49uvH43XffzSgSgPQ1Go3QarVCCCFUq9XQbDZvff14PA57e3u+MwHWbt0XLc06b37zzTfXut1VxDKvR92UWMkbyZbts/Yn28BxflNMNTDjDUhHDHkuhhiAzVPDABalfgHMS/0CshXDWD+Gz/8YYoC8iCFvpCWWthiDUGSx9LO0qHcAaZEXksmzEDd97Sa1bWBdYsi3McQAbK9YaorGWMCi1LaAPFHbAkKI4/wrhrFQDDEAi4khf6UllrYYk8H6xdLf06IWtrhS1gEAAAAA5E2327360fZyuaxgDWyVcrkcDg8Pw/n5eahWqzNf58eGgbwZDofh6OgohBBCp9MJlUol44gA8qfX6yVOwBgMBpsPBmABZ2dnic/fdt57lwcPHiQ+Px6P5UWg0Pr9/o3HjUYjo0gA0jMej8Pe3t5VjqvVauHk5CR0Op25LsBoNBpT+REgTffv389ku+u+GGtZsc3rUTclRvLGbMv0WfuTbeA4vym2GpjxBqwuhjwXQwzAZqlhAMtSvwDmoX4B2YllrB/D538MMUAexJI30hBbW4xBKKLY+lla1DuANMgLs8mzEC997Sa1bWBdYsi3McQAbKfYaorGWMCi1LaAvFDbAmI5/4phLBRDDMD8YslfaYitLcZksD6x9fe0qIUtppR1AAAAAAB5Mh6PQ6vVunr80Ucf+eF2YCuVy+Vbc+BwOAzj8XizQQGs4J133gkhvPphzWazmXE0APlULpfDgwcPEv82Go02HA3A/Gadv7755ptLr7Narc48Zy7KRD2AScPh8Ma4r1wuh1qtlmFEAKsbjUZhb2/v6sKLWq12YzxXr9fD6elpqFart66n0Wi4EApYm3VfnHR2dpb4fIzzZWKc16NuSozkjdmW6bP2J9vAcf61GGtgxhuwuhjyXAwxAJujhgGsQv0CuIv6BWQnprF+DJ//McQAsYspb6wqxrYYg1A0MfaztKh3AGmQF2aTZyFe+trX1LaBdYoh38YQA7B9YqwpGmMBi1LbAvJAbQuI6fwrhrFQDDEA84kpf60qxrYYk8F6xNjf06IWtphS1gEAAAAA5Mnlj7aHEEKv17vzR5YAiqxcLoeTk5OZRXY/MgfkRaPRCOPxOJTL5dDr9bIOByDXms1m4vPj8XizgQCkYNVJZfV6PfF558tAUT169OjG46wvDgVY1Wg0Cnt7e1cXIcyqH1YqlXBychLa7fat62s0Gi6EAtbi/v37M/+2zrrcbdvNSqzzetRNiY28cbtF+6z9yTZwnH8t1hqY8QasJoY8F0MMwOaoYQCrUr8AbqN+AdmJaawfw+d/DDFA7GLKG6uKtS3GIBRJrP0sLeodwKrkhdvJsxAnfe1ratvAOsWQb2OIAdg+sdYUjbGARaltAbFT2wJiOv+KYSwUQwzAfGLKX6uKtS3GZJC+WPt7WtTC5lfKOgAAAACAvGi1WmE4HIYQQuh0OjN/XBNgm5TL5fDgwYPEv/mBOSAP+v1+6Pf7IYQQPvjgg5V/gB1g25XL5cRJKGdnZxlEAzCfSqWS+PyqE8fefvvtxOedLwNFdXl+fem9997LKBKA1Y3H47C3t3djTNjr9W6tHx4eHobj4+Nb19loNFKMEuCVdX+3Mev8OLbvVGKe16NuSmzkjdst2mftT7aB4/xrsdbAjDdgNTHkuRhiADZDDQNIg/oFcBv1C8hGbGP9GD7/Y4gBYhZb3lhFzG0xBqEoYu5naVHvAFYlL9xOnoU46WtfU9sG1imGfBtDDMB2ibmmaIwFLEptC4id2hZst9jOv2IYC8UQA3C32PLXKmJuizEZpCvm/p4WtbD5lbIOAAAAACAPut1u6Ha7IYRXRbVms5lxRADxmJUTT09PNxwJwGLG43F4//33QwghVKvVUKlUwnA4XOpf0g+sj0ajma9f9YfeAWJWq9WyDgFgIeuaxJU0gS2E2ZPJAPJsNBpNnRsXcYIysD3eeeedG+O2arU61/lurVYLp6enM8eYw+Fw6oJ6gDTMOgdN+v5iEbedw1YqlZXWnaY8zOtRNyU225437rJon7U/2QaO8/hrYMYbsJoY8lwMMQDrpYYBpEn9AkiifgHZiHWsH8PnfwwxQIxizRvLyENbjEHIuzz0s7SodwCrkhduJ89CnPQ1tW1gM2LItzHEAGyHPNQUjbGARaltAbFS24LtFuv5VwxjoRhiAGaLNX8tIw9tMSaDdOShv6dFLWw+pawDAAAAAIjdYDAIrVYrhBDC4eFhoYtqAMsol8uJufHs7CyDaADmNxqNrr7MGw6HYW9vb+l/g8Fgav39fn/m6x8/frzh1gJszu7u7tRz9+/fzyASgPm8+eabic9//PHHK603hslhAJvS6XRuPI7p4lCARfX7/TAcDm88d/l98TwqlUo4OTkJ5XI58e8PHz5cJTyARLMuolr1O9tZy8+6CCsLeZnXo25KbLY5b8xj0T5rf7INHOfx18CMN2A1MeS5GGIA1kcNA0ib+gWQRP0CNi/msX4Mn/8xxACxiTlvLCovbTEGIc/y0s/Sot4BrEpeuJ08C3HS19S2gc2IId/GEANQfHmpKRpjAYtS2wJipbYF2yvm868YxkIxxAAkizl/LSovbTEmg9Xlpb+nRS1sPqWsAwAAAACI2Wg0Co1GI4QQQrvdDu12O+OIAOK0t7c39ZwfIQYA2E5JkzNm/SAxQAxmnb+Ox+PNBgKQY/1+/8bj9957L6NIAFb38OHDqefefffdhdZRqVRCr9dL/NtwODTWBFL39ttvJz4/Go1WWu+s5WddhLVpeZrXo25KbLY1b8xr0T5rf7INHOfx18CMN2A1MeS5GGIA1kMNA1gH9QsgifoFbFbsY/0YPv9jiAFiEnveWESe2mIMQl7lqZ+lRb0DWJW8cDt5FuKkr6ltA5sRQ76NIQag2PJUUzTGAhaltgXESm0LtlPs518xjIViiAGYFnv+WkSe2mJMBqvJU39Pi1rYfEpZBwAAAAAQq/F4HPb29sJ4PA7NZjMcHh5mHRJAtJJ+yPjNN9/MIBIAAGKUNF4EiMWsiVyrThybxeRXoGhGo9FUzqzX6xlFA7C64XA49dwyY7harTYzHw4Gg4XXB3CbWee2p6enK613PB4nPr+/v7/SetNQhHk96qZkaRvzxqpu67P2J9tg24/zvNbAjDdgfjHkuRhiANKnhgFskvoFbDf1C9isPIz1Y/j8jyEGiEUe8sa8itAWYxBiV4R+lhb1DmAR8sLi5FnI3rb3NbVtYFNiyLcxxAAUVxFqisZYwKLUtoCsqW3BdsrD+VcMY6EYYgBuykP+mlcR2mJMBvMpQn9Pi1rYtFLWAQAAAADE6HpRrV6vh06nk3VIAFFLKsD7Mg8AYDudnZ3deFytVjOKBGA+5XI58Rz28ePHa9ne/fv317JegKz0+/0bj2dNyAXIg8kL3kNY7fuOWRdvTJ47A6yqXC6Hcrk89fxwOFxpvT/72c8Sn3/rrbdWWu+q8jivR92U2Gxb3ljUon3W/mQbbPtxnocamPEGrCaGPBdDDEC61DCAdVK/ACapX8Dm5GWsH8PnfwwxQAzykjfmkce2GIOQN3nsZ2lR7wBWJS/cTp6FOG17X1PbBjYlhnwbQwxAMeWxpmiMBSxKbQuIkdoWbJ+8nH/FMBaKIQbga3nJX/PIY1uMyWA5eezvaVELm08p6wAAAAAAYnNZVBuNRqFer4der5d1SADRG4/HU8/FOBEM4LpqtRouLi5S+ddut6fW3263Z75ejgSK7PT09MZjOQ/Ig6TJZUnnuuvaFkCeTU5ObjQaGUUCsLqkMWDSRQbzqlQqoVKpzLUdgFU1m82p5x4/frzSOpMuqqpWqyvlxlXldV6Puikx2pa8sYxl+qz9yTbY5uM8DzUw4w1YXQx5LoYYgHSoYQDrpn4BTFK/gM3I21g/hs//GGKALOUtb9wmr20xBiFP8trP0qLeAaRBXphNnoV4bXNfU9sGNimGfBtDDECx5LWmaIwFLEptC4iR2hZsl7ydf8UwFoohBiB/+es2eW2LMRksLq/9PS1qYfMpZR0AAAAAQGzeeeedMBqNQq1WS6WoNhwO/bgSUHhnZ2c3HsdUCAcAYLMmJ0rs7+9nFAnA/N57773E5weDQerbkheBIhmNRmE0Gt147t13380oGoD1WPW73mq1mk4gAHdotVpTz43H45XyWNJFVbPOoTclr/N61E2J0bbkjWUs02ftT7bBth7neamBGW/A6mLIczHEAKRDDQNYN/UL4Dr1C9icvI31Y/j8jyEGyFLe8sZt8toWYxDyJK/9LC3qHUAa5IXZ5FmI17b2NbVtYNNiyLcxxAAUS15risZYwKLUtoDYqG3B9snb+VcMY6EYYgDyl79uk9e2GJPB4vLa39OiFjafUtYBAAAAAMRkf38/DIfDUKvVwvHx8crrG4/H4Z133kksEgEUyWTOjKkQDgDAZg0Gg6v/VyqVUKvVMowGYD71ej2Uy+Wp51eZeDc5ge2SvAgUSb/fv/G4Wq0m5lOAvEjKYWdnZyuts1KpzPUcwKoqlUqoVqtTz1+v1y1iNBolXlDVbDaXWl8a8jyvR92UGG1D3ljWMn3W/mQbbOtxnpcamPEGrC6GPBdDDMDq1DCATVC/AK5Tv4DNyONYP4bP/xhigKzkMW/Mkue2GIOQF3nuZ2lR7wDSIC/MJs9CvLa1r6ltA5sWQ76NIQagOPJcUzTGAhaltgXERm0Ltksez79iGAvFEANsuzzmr1ny3BZjMlhMnvt7WtTC5lPKOgAAAACAWOzv74fBYBCq1WoqRbUQQnj//ffD/fv3FbWBwrteSC+Xy6HdbmcYDQAAWel2uzceHx4eZhQJwOKSJnV9+OGHS69vNBpNPVer1fwQO1Aojx49uvG41WplFAlAOpLGauPxOPGigHklLZt00QJAGpLGY5NjtnlN3gwkhFfnzlndECTP83rUTYlZkfPGslbps/Yn22Abj/M81MCMNyA9MeS5GGIAlqeGAWyC+gUwSf0C1i/PY/0YPv9jiAE2Lc95Y1Ke22IMQl7kuZ+lRb0DSJO8ME2ehfhtY19T2wayEEO+jSEGIP/yXFM0xgIWpbYFxEhtC7ZHns+/YhgLxRADbKs8569JeW6LMRksJs/9PS1qYQu4AAAAtl65XL4IIdz4V6lUsg4LYKPq9fpV/js/P09lnc1m8yKEcHF4eJjK+gBidXJycmMs2ev1sg4JYOPa7fbUuXW73c46LICNq1QqV3mwWq1mHQ7AQs7Pz6fGdKuc517WHK//Oz4+TjlqgOycnp5O5bm0vmMByFLSOK7T6Sy9vlqtZk4OsFFJ8wGXcb3Wd/nv9PR0oXW02+2reGq12sLLX8r7vB51U2JXxLyxilX7bEz7E9YlpuN83XkjLzUw4w3yYlPXL62aG2LIczHEADHIS964pIYB2cpbzliF+gWkoyh5Q/0C1i+Gsb56RzoxwKYUIW9ciqEtqzAGIQ9i6GfqHclxGGtAvsWUF+TZ5DjkWZgWU19T237FeSUsJi/fv8WQb2OIAfhaXvLXpRhqiqswxoJ05C13rUJtC4qjKLlLbQu2RwznX2ph6cQA26YI+etSDG1ZhTEZzC+G/q4WlhxHrGOvUgAAAADYcq1WK/T7/VCpVMLJyUkol8tLr2s8HofBYBD29/dDt9sNIYTQbDZTihQgTgcHB1f/r9froV6vZxgNAACLGgwG4eDgIBwcHITBYLD0eo6OjsJoNAohhFAul8NHH32UVogAG1Eul8Ph4eHU8w8fPlxqfZM5tVqthlqtttS6AGLU7/dvPK5Wqyt9xwIQi1arNfVc0jhxXpPjQt+jAOv24MGDqecu57DMazgcXtX6LrXb7VCpVOZeR6vVCkdHR2E8HocQXuXDvb29q8eLrCeLeT3qpmyTIuSNmPpsLPsT1imW4zyt8cZt1lkDiyl3QZGkkRtiyHMxxADbQg3jFWMKmI/6xdeMNWA+6hevGGuQZzHch0C9I70YYBOKkjcu16PeAeuV95wRU3811gAmxZIX5NmvybNwt1j6mtr2K84rIU5q5unFAGyW2v0rxliQL2pbXzP2gvxQ23rFuAtWl/c5HZdiGAvFEANsk6Lkr8v1qIXBdsh77oopb2zV2OsCAADYeiGEqX/lcjnrsAA2ot1uJ+bBtP7V6/WsmwiQqNfrXZTL5YsQwkWlUrloNpsX5+fnC6/n8PDwKufVarX0AwXIiaRxZbvdzjosgDtdH89d/qtUKhe9Xm+h9RwfH99Yx8nJyZoiBli/arU6lRsPDw8XWken05lax+np6ZoiBsjGZL5cNFcCxKxWq02N5xY9V764mK4bmo8DbMrkWG3R/DO5fKVSWWj58/PzmXNpFvn+JKt5PeqmbKM8540Y+2zW+xM2IevjPK3xxqJxplUDizF3wSYk9dk06yVp5oas81wsMUDW8pI31DAgDjHnjBj7q7EGxJ03FqF+AesTw30I1DvSjwHWqUh5Q70D1i/vOSPG/mqsAUzKOi/Is7cvL89Csqz7mtr2K84rYTlJuSPW79+yzrexxAC8kpf8pXYPXBdz7ooxbxh7QRxizl2LUNuC4sv7nI5JMYyFYogBtkGR8pdaGGyPvOeuGPPGtoy9SgEAANhqg8Eg8fnxeLzZQAAycHR0FI6Ojta6jVartdb1Ayyr0WhcjflGo1HodrthZ2cnHBwczL2Obrd79fparRaOj4/XESoAAGvU6XSmnhuNRqHRaIT9/f256oSDwSDs7++HEEKoVCrh9PQ0VKvVtEMF2JherxfK5fKN5w4ODsJwOJxr+fF4PHV+3ev1QqVSSStEgMyNx+OpvFiv1zOKBiB9nU5nakzYaDTCaDSaex2j0Wjq++her5dGeAB3mjy3TTpXnaXb7U6N9Rb9Lvi2fDlvLs1yXo+6Kdsoz3kjxj6b9f6ETcj6OE9jvHGXddbAYsxdsG6buH4pzdyQdZ6LJQbIUl7yhhoGxCH2nBFjfzXWYNvFnjfmpX4B6xPLfQjUO9KPAdalSHlDvQPWrwg5I8b+aqwBTMo6L8izX5NnYX5Z9zW1beeVsKy8ff+Wdb6NJQYgP/lL7R64LvbcFWPeMPaC7MWeu+altgXFV4Q5HZNiGAvFEAMUXZHyl1oYbI8i5K4Y88bWjL0uAACArVatVi9CCIn/Dg8Psw4PYG06nc7M/JfWv0qlknUzARKdn5/fmb96vd7M5U9PTy/q9bpxI8A17XZ7Kp+22+2swwK40231wRDCRblcvuh0OonLnp+fXzSbzavX1mq1i/Pz8802AGBNTk9PL8rl8lRevO18+eLiVW6czK13LQOQR4eHh74TAQrv5OQk8Tz5+Pj4zmWPj4+nxpOzzq8B1iXp3PauXHR8fDyV++bJe5Nu+056nu9Psp7Xo27Ktspr3oi1z2a5P2FT8po35rXOGlisuQvWaRPXL6WdG2L4PI8hBshKHvKGGgbEI/acEWt/NdZgm8WeN+alfgHrkfVY/zr1jvXEAGkrUt7Iui3GIGyDrPvZdeodrxhrQLHldX6LPAvbLa+5a15q21BMefz+LYaxTQwxwLbLQ/7KuqZojAXxiT13xZo3jL0gW7HnrnmpbUGxZX3+dZ1a2HpigKIqUv7Kui3GZLA5Wff369TCXsnb2CtkHQAAALB5p6enF4eHhxeVSuXOk8J2u31xfHysQAMUSq/XW3tRLYT0JnIArMNdhfnLLwiazeZFp9O56HQ6F+12+8Zy9Xr94vT0NOumAESh3W4vNcEDIGvzniOXy+WLer1+cXh4eNFsNm+MCyuVih8YBgrp/Pw88fy5VqtdnJycTL220+ncmGw27w+3A+TRZH50DgwU1enpaeKYsF6vJ471Tk5OblzcYFw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      "text/plain": [
       "<Figure size 9000x1200 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
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       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Fitting stars:   0%|          | 0/28473 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
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      "text/plain": [
       "<Figure size 9000x1200 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
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       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Fitting stars:   0%|          | 0/34561 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
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c636gSERaPz4CZK3dbseNGzci4nm+Ozw8HGlAw8HBQSwvLw/8+/7+ftTr9UnDBJi6swFZ4xavFxcXo9Vq9Uw/PDz0gx5Qemc5tFqtRq1W6xjgGuEhm0CxXRxQsr29HaurqzlHBJCvfoPJIiJWV1dje3s7h4gApuPiwNdxL97sp/v36JOTk4kuNAWYtn4XAoybu7ovjjceB5iVizf8ODNOLstqOeNIdXyP+illVIac0U9ex2tZtydcVPT9POU6mL4GZVeU65dSyHMpxAApSD1vqF9AWlLPGf2oX0C+Us4b6heQr1T7+pNI4fs/hRhgWsqUN1Jtiz4IZZLqcZYV9Q4gJWXNDXItlFvRjzX1bSDl3+AuSiHfphAD8FzquSvVmqL+FeQr9dzVj7oWEJF2/lLbAiLSPQebRAr9oRRigDIrU+5KtS36Y5C9VI/3rKiFTd9C3gEAAAD5S+kkBWAWdnZ2zv+/v78/ch6s1+uXPnRzd3d33NAAZqbdbsfe3l6srKzE+vr6WMvY3NzsO73Vak0SGkDy9vb2zh+oubu7Gzdv3sw5IoBs3b59OyKe1w0N8ALm3c7OTqytrfVMX1lZubRGCFBEZ/3A7e3tzC4KPTg46Hhdr9f9Pg0k7/333++ZNm7uqlarHa/9hgLMwt7eXs/FTOP2w95+++2eaWf9xmlLdXyP+illU5ac0U8ex2uZtyecKcN+nnIdTF+DsitCfTiFPJdCDJCK1POG+gWkJfWc0Y/6BeQr5byhfgH5SrWvP64Uvv9TiAGmqUx5I9W26INQJqkeZ1lR7wBSUebcINdCeZXhWFPfBlL+De5MCvk2hRiAL6Seu1KtKepfQb5Sz139qGsBEWnnL7UtICLdc7BxpdAfSiEGKLsy5a5U26I/BtlL9XjPilrY9C3kHQAAAJA/DxEG5s1ZQWx7e7vnYUjDWl1djVqt1vdvH3zwwdixAczK7du3o1KpxHvvvTf2MrIaHAZQJO12O959992IiFhfXx/YJwQoqouDJjY3N/MNBiBne3t7sba21jO9VqvlPrAOIGutViuazWasrKxkOmC3e5Byo9HIbNkA09JqtXqmNZvNsZb16quv9kzrvlgBIGv9Llwatx/Wb76tra2Z5LIUx/eon1JGZckZ3fI6Xsu6PeGiou/nKdfB9DWYB0W4fimFPJdCDJCK1POG+gWkJfWc0U39AvKXat5Qv4D8pdjXn0QK3/8pxADTVKa8kWJb9EEomxSPs6yodwApKWtukGuh3Ip+rKlvAxHp/gZ3UQr5NoUYgC+knrtSrCnqX0H+Us9d3dS1gDOp5i+1LeBMiudgk0ihP5RCDFB2ZcpdKbZFfwymI8XjPStqYbOxkHcAAAAAALPUbDaj1WpFtVqdeGDDoKJVSsUfgEH29vbivffei0qlMtFy+s0/7g8WAEXQaDSi3W5HrVYz+AEopbNBE5VKJdMLAgCKptls9h38ValU4sMPP8whIoDp2t7ejkqlEu+9916myz04OOh4/fbbb2e6fIBp6Pd7b6vVGmtZR0dHPdMm/W0G4DLNZjOazWbP9Hq9PtbyBs23s7Mz1vKGler4HvVTyqYsOaOfPI7XMm9POFOG/TzlOpi+BuQvhTyXQgzAcNQvgEmpXwCDqF9AvlLt648rhe//FGKAaSpT3ki1LfoglEmqx1lW1DuAVJQ5N8i1UF5lONbUt4EiSCHfphADUByp1hT1r4BRqWsBqVPbAiLSPQcbVwr9oRRigLIrU+5KtS36Y5C9VI/3rKiFzcZC3gEAAAAAzNLZAIQsHqR+WdEoz8IawDCOjo5iZWVlKsuuVqtTWS5A3nZ2ds77k7u7uzlHA5C9g4OD80ETt27dyjkagPy02+1oNBp9/7a5uelh6kApbW5uxuHhYaY57uDgoOP3klqtJocChdAvV73//vtjLavVanW89hsKMG1nF2N1myT/9Jt33Lw4rBTH96ifUkZlyRnd8jpey7o94aIy7Oep1sH0NSANKeS5FGIAhqN+AUxC/QK4jPoF5CvFvv4kUvj+TyEGmKYy5Y0U26IPQtmkeJxlRb0DSElZc4NcC+VWhmNNfRsoghTybQoxAMWRYk1R/woYlboWUARqW0BEmudgk0ihP5RCDFB2ZcpdKbZFfwymI8XjPStqYbOzkHcAAAAAALP0/vvvR6VSiZWVlUyWN6iw5uFywLzo/hFhZWVFDgRKqdVqxdraWkREbG9ve4gmUEoXB6BsbGzE4uJiNBqN2NnZOR/EATAP3n333Z6HqEc8v6BpdXU1h4gAZiPrc93d3d2O12fn1QCp65cP9/b2+vYRr/LRRx91vK7VamPHBTCMs4vNLpo09/Sbv9lsTvWCsxTH96ifUkZlyRnd8jpey7o94aKy7Ocp1sH0NSANKeS5FGIAhqN+AUxC/QK4ivoF5CfFvv4kUvj+TyEGmKYy5Y0U26IPQtmkeJxlRb0DSElZc4NcC+VWlmNNfRtIXQr5NoUYgOJIsaaofwWMSl0LKAq1LSDFc7BJpNAfSiEGKLsy5a4U26I/BtOR4vGeFbWw2VnIOwAAAACAWbp161bPQIRJ9Cue5VFQA8hDv4L9rVu3cogEYPoajUZEPP9R1QPZgTJqNps9gyZarVbs7e3F2tpaLC0txY0bN6LRaMTe3l5OUQJMX7PZHJjn3nvvvRlHA1BsH3zwQcfrt99+O6dIAEYz6EL5sxrhsHZ2dnouGhjnInmAYbVarb4XK73xxhsTLffNN9/sO727v5el1Mb3qJ9SRmXKGRfldbyWdXvCRfbzwSatg+lrQBpSyHMpxAAMT/0CGJf6BZAH9QsYXmp9/Umk8P2fQgwwbWXKG6m1RR+EMkrtOMuKegeQkrLmBrkWys2xNpj6NpClFPJtCjEAxZJaTVH/ChiVuhYwz9S2oHhSOwebRAr9oRRigHlQptyVWlv0x2B6Ujves6IWNlsLeQcAAAAAMEsrKytRr9czW97Nmzd7pg16WBNA2bz//vsdrzc3N6NWq+UUDcD0bGxsRLPZjEqlkukPtAApuX379pXvabfbsbe3F41GI65duxaNRiNardYMogOYnXfffbfv9Fqt5pwXYAQHBwcdg3JrtVoug5IBxvHOO+/0nd5sNmNtbW3o5Wxubna8zvq3aoBu3RdjnVlcXJxouYPOh/f39yda7mVSG9+jfkoZlSlnXJTX8VrW7QkX2c/7y6IOpq8BaUghz6UQAzA89QtgXOoXwKypX8BoUuvrTyKF7/8UYoBpK1PeSK0t+iCUUWrHWVbUO4CUlDU3yLVQbo61/tS3gaylkG9TiAEoltRqivpXwKjUtYB5pbYFxZTaOdgkUugPpRADzIMy5a7U2qI/BtOT2vGeFbWw2VrIOwAAAACAIjs+Pu6ZlkdRDWDW2u127OzsnL9eXV2N9fX1HCMCmI5msxlbW1sREfHee+95kDBQSmeDMEa1t7cXi4uLsba21jHoH6CoDg4Ootls9v3brVu3ZhwNQLHt7u52vH7nnXdyigRgdLVabeCFGjs7O7G2tnblMtbW1joucKhWq/Hee+9lFiNAP4MuVJp0HEu/C84iYuA5dIomGd+jfkpZlTFn5Hm8lnF7Qjf7eX+T1sH0NSAdKeS5FGIA8qN+AfNB/QLIg/oF5CvPexGk8P2fQgxQNGW6h4l6B0xfCjlDvQNITRlzg1wL5edY6099G8haCvk2hRiA+aZ2D8ySuhYwz9S2gAhjSFOIARhdCmPSsqIWBvMjhdylFjZ7C3kHAAAAAFBkFx+odMYD5oB5sLGxcV6QX19fj+3t7XwDApiSRqMRERErKyuxsrKSczQA03H79u2J5t/Z2Ylf/dVfjYODg4wiAsjH5ubmwL/pCwKM5oMPPuh4LY8CRbO9vR2VSqXv33Z2ds7rhoP+vrOzc/66Wq3G4eHhwOUBZGXQhUqT5p9BF1b1GzOTqknG96ifUlZlzBl5Hq9l3J7QzX7e36R1MH0NSEcKeS6FGID8qF/AfFC/APKgfgH5yvNeBCl8/6cQAxRNme5hot4B05dCzlDvAFJTxtwg10L5Odb6U98GspZCvk0hBmC+qd0Ds6SuBcwztS0gwhjSFGIARpfCmLSsqIXB/Eghd6mFzd5C3gEAAAAAFFm/olK9Xs8hEoDZ2draOn+o3O7u7qUPLwYoskajEa1WKyqVSrz33nt5hwMwNYuLi1Gv16NWq409SKLdbsfy8nLHw4cBiqTVag0cdNZd79vb24tGoxE3btyIa9eunf9bXFyM5eXl2NraSmZwGEAems1mtNvt89fVanXgYFqAVFWr1djd3R349729vVhcXOzp921sbMTa2tr563q9HkdHRxNflAAwjEHnopP2xS7LYUU5/51kfI/6KWVVxpyR5/Faxu0J3eznvbKog+lrQDpSyHMpxADkR/0C5oP6BTBr6heQvzzvRZDC938KMUDRlOkeJuodMH0p5Az1DiA1ZcwNci2Un2Otl/o2MA0p5NsUYgDmm9o9MEvqWsC8UtsCzhhDmn8MwOhSGJOWFbUwmB8p5C61sNlbyDsAAAAAgKLqV1BbXV31YCWg1DY2NmJjYyMiIlZWVgr7IyjAVfb29mJvby8iInZ3d/XxgFJbXV2N/f39ODw8jJOTkzg9PY3Dw8PY3Nwcub+3trZ2nj8BiuSy3LW8vBwRETs7O3Hjxo1oNBqxt7fXcdFTxPPBYAcHB7GxsRGLi4vRaDSSGCAGMGvb29sdr1dWVnKKBGAy9Xq9J6dd1Gq1YnFxMXZ2ds4vYtja2jr/+/b2duzv788iVICec9SLbt68OfHyB/1O0m/sTGomHd+jfkoZlTVn5HW8lnV7wkX28/6yqIPpa0AaUshzKcQA5Ef9AuaH+gUwa+oXkK8870WQwvd/CjFA0ZTpHibqHTB9qeQM9Q4gJWXNDXItlJtjrT/1bSBrKeTbFGIA5pvaPTBr6lrAvFLbAiKMIU0hBmB0qYxJy4JaGMyPVHKXWtjsLeQdAAAAAEBRvf/++z3TNjY2cogEYPparVbPQ+X29vbixo0bch9QOu12O959992IeP4D5qg/VAKUQa1Wi/X19djf34/T09PY3d0dOh82Go0kBkQAjKJfre+ixcXFWFtbu3SgWbe9vb1YXFw0+BWYOx988EHH63feeSenSAAmt7q62nPBe7e1tbW4ceNGHBwcnM9zcnISq6urswgRICIijo+PB/6tiBe2Zmka43vUTym6ecoZszhe52l7Mr/s5/1Nqw6mrwGzl0KeSyEGID/qFzDf1C+AaVK/gHzleS+CFL7/U4gBiqZM9zBR74DpSzlnqHcAeZmn3CDXQnk41vpT3waylkK+TSEGYL6p3QMpUNcC5oHaFhBhDGkKMQCjS3lM2qjUwmB+pJy71MKmayHvAAAAAACKqvuhmqurq1GtVnOKBmA62u12rK2txeLi4vlD5bptbW3FjRs3otVqzTg6gOloNBrRbrejWq1e+eBNgHmxsrIS+/v7cXR0FCsrK1e+/6233op2uz39wAAyctkgs42NjWi1WrG6uhq7u7txeHgYJycncXp6GkdHR7G9vX3pgLZGoxFbW1vTCBsgOc1ms6MfWKlUolar5RcQQAbO+oHDvnd7e7v0FyEA6cnrt9rLLshKxSzG96ifUjTznDOmcbzO8/ZkftjPe82yDqavAdOXQp5LIQYgP+oXwEXqF0BW1C8gf3neiyCF7/8UYoCiKdM9TNQ7YPqKlDPUO4BZmefcINdCcTnWeqlvA9OQQr5NIQZgvqndAylS1wLKRm0LOGMMaf4xAKMr0pi0q6iFwfwoUu5SC8vWQt4BAAAAABTRwcFBR1GpUqnE5uZmjhEBZOvg4CAajUbcuHEjdnZ2rnx/u92OxcXFODg4mEF0ANOzs7NznsuGfeAmwDypVquxu7sbR0dHlw4sabfbcfv27RlGBjC+ZrN56d9XV1fj5OQktre3Y2VlJWq12vnD1qvVaqyursb+/n7s7+8PfAj7xsaGc2ZgLrz//vsdr1dXV3OKBCBbZxcxXGVnZycajcYMIgLoNO0LLm/evJnLeic16/E96qcUhZyR7fFqezIP7Oe98qiD6WvA9KSQ51KIAciH+gUwiPoFMCn1C8hX3vciSOH7P4UYoEjyzhtZUu+A6StqzlDvAKZNbpBroYgca73Ut4FpSCHfphADML/U7oHUqWsBZaG2BUTkP64jhf5QCjEAo8k7d2VJLQzmR1Fzl1pYNhbyDgAAAACgiLoLaO+9997AB28CFM3S0lIsLy/H3t7eyPMuLy93/OgAUCStVivW1tYi4nl/r1ar5RwRQLqq1WocHR1dOtB/a2sriYERAFf56KOPBv5tfX09tre3h6r91ev1ODw8HPjeRqMhLwKlt7Oz0/H6nXfeySkSgOxd1d87s7e3F4uLi34vAWbq+Pg4l/V+9tlnuax3WHmN71E/JXVyxheyOF5tT+aB/bxXnnUwfQ3IXgp5LoUYgHyoXwBXUb8AxqV+AfnK+14EKXz/pxADFEneeSNL6h0wfUXPGeodwLTIDV+Qa6E4HGu91LeBaUgh36YQAzC/1O6BolDXAopObQuIyH9cRwr9oRRiAEaTd+7KkloYzI+i5y61sMks5B0AAAAAQNE0m804ODg4f72yshIrKys5RgSQrQ8//DBOTk7i5OQkjo6O4vDwMHZ3d2N1dXWoHxCWl5enHyTAFDQajYiIqNVqsb6+nnM0AMWwvb19ac7svjAAIEVHR0cD/9Y9uO4q1Wo1dnd3+/6t3W7Li0CpNZvNjsG6lUolarVafgEBTMFHH3001AVNrVYrlpaWotlsTj8ogIi4efPmVJdfpAvNzqQwvkf9lFTJGb0mOV5tT+aB/bxTKnUwfQ3ITgp5LoUYgNlTvwBGoX4BjEL9AvKVQl8/he//FGKAokghb2Qlhbbog1B2KRxnWVHvALImN/SSayF9jrVO6tvAtKSQb1OIAZhPKdQU9a+AUalrAUWktgVEpHEOlkJ/KIUYgOGlkLuykkJb9MdgNlI43rOiFjaehbwDAAAAACiad9999/z/lz1sE6CoKpXK+b9qtRq1Wi1WVlZie3s7fvjDH15ajI94/sC5vb29GUULkI2NjY3zB2Xq3wGMZnNzM+r1et+/7e/vzzgagNENerj6oNx2lXq9PnAQ3u3bt8daJkARvP/++x2v33777ZwiAZiORqMRa2trERFRq9VidXX10ve32+1YWlrymwkwE9O+cGnQufOrr7461fVOIpXxPeqnpEjO6G/c49X2ZB7YzzulVAfT14BspJDnUogBmD31C2BU6hfAsNQvIF8p9PVT+P5PIQYoihTyRlZSaYs+CGWWynGWFfUOIEtyQ39yLaTNsdZJfRuYlhTybQoxAPMplZqi/hUwKnUtoGjUtoCINM7BUugPpRADMLwUcldWUmmL/hhMXyrHe1bUwka3kHcAAAAAAEWys7Nz/tD2SqWiWA3MnUqlEpubm3FychK1Wm3g+zxsGCiSZrMZW1tbERGxvb0d1Wo154gAimd3d7fv4IuDg4PZBwMwouPj477TLzvvvcqtW7f6Tm+323IjUFp7e3sdrxuNRk6RAGSr3W7H0tLSeZ6r1+txeHgY29vbQ12A0Wg0enIkQNZu3ryZy3qnfUHWuFIb36N+SmrkjMHGOV5tT+aB/bxTanUwfQ2YXAp5LoUYgNlSvwDGpX4BDEP9AvKTSl8/he//FGKAIkglb2Qhtbbog1BGqR1nWVHvALIiNwwm10K6HGud1LeBaUkh36YQAzB/Uqsp6l8Bo1LXAopEbQtI5Rwshf5QCjEAw0kld2Uhtbboj8H0pHa8Z0UtbDQLeQcAAAAAUBTtdjvW1tbOX3/44Yce3A7MrUqlcmkebDab0W63ZxsUwJjeeuutiHj+UM3V1dWcowEopkqlErdu3er7t1arNeNoAEYz6Pz11VdfHXuZtVpt4DlzWQbqAVzUbDY7+n2VSiXq9XqOEQFko9VqxdLS0vmFF/V6vaM/t7KyEkdHR1Gr1S5dTqPRcCEUMFXTvkDp+Pi47/QUx82kOL5H/ZTUyBmDjXO82p7MA/v5F1Ksg+lrwORSyHMpxADMjvoFMAn1C+Aq6heQn5T6+il8/6cQA6QupbwxqRTbog9C2aR4nGVFvQPIitwwmFwL6XKsfUF9G5imFPJtCjEA8yXFmqL+FTAqdS2gKNS2gJTOwVLoD6UQA3C1lHLXpFJsi/4YTEeKx3tW1MJGs5B3AAAAAABFcfbQ9oiI3d3dKx+wBFB2lUolDg8PBxbZPWQOKIJGoxHtdjsqlUrs7u7mHQ5Aoa2urvad3m63ZxsIQEYmHVS2srLSd7rzZaCM3n///Y7XeV8UCpCFVqsVS0tL5xchDKohVqvVODw8jPX19UuX12g0XAgFTM3NmzcH/m2a9bnL1puXVMf3qJ+SEjnjcqMer7Yn88B+/oVU62D6GjCZFPJcCjEAs6N+AUxK/QK4jPoF5Celvn4K3/8pxACpSylvTCrVtuiDUCapHmdZUe8AsiA3XE6uhTQ51r6gvg1MUwr5NoUYgPmSak1R/woYlboWUARqW0BK52Ap9IdSiAG4Wkq5a1KptkV/DLKX6vGeFbWw4S3kHQAAAABAEaytrUWz2YyIiO3t7YEP1gSYN5VKJW7dutX3bx4wB6Rub28v9vb2IiLivffem/jh6wDzrlKp9B2Acnx8nEM0AMOrVqt9p086cOzNN9/sO935MlBGZ+fXZ955552cIgHIRrvdjqWlpY4+4e7u7qU1xM3Nzdjf3790mY1GI8MoAb4w7d84Bp0jp/bbSsrje9RPSYmccblRj1fbk3lgP/9CqnUwfQ2YTAp5LoUYgNlQvwCyoH4BXEb9AvKRWl8/he//FGKAlKWWNyaRclv0QSiLlI+zrKh3AFmQGy4n10KaHGtfUN8GpimFfJtCDMD8SLmmqH8FjEpdCygCtS2Yb6mdg6XQH0ohBuByqeWuSaTcFv0xyFbKx3tW1MKGt5B3AAAAAACp29nZiZ2dnYh4XlBbXV3NOSKAtAzKi0dHRzOOBGB47XY73n333YiIqNVqUa1Wo9lsjvWv38PVW63WwPdP+pB3gJTV6/W8QwAY2bQGcfUbwBYxeDAZQFG1Wq2ec+MyDk4G5stbb73V0W+r1WpDnfPW6/U4Ojoa2MdsNps9F9MDZGXQeWi/3zFGcdl5bLVanWjZWSrC+B71U1Iy7znjKqMer7Yn88B+nn4dTF8DJpNCnkshBmC61C+ALKlfAP2oX0A+Uu3rp/D9n0IMkKJU88Y4itAWfRCKrgjHWVbUO4AsyA2Xk2shTY419W1gNlLItynEAJRfEWqK+lfAqNS1gJSpbcF8S/UcLIX+UAoxAP2lmrvGUYS26I9BNopwvGdFLWw4C3kHAAAAAJCyg4ODWFtbi4iIzc3NUhfUAMZVqVT65sfj4+McogEYTqvVOv8hr9lsxtLS0tj/Dg4Oepa/t7c38P0fffTRjFsLMDuLi4s9027evJlDJADDe/XVV/tO/+yzzyZabgqDwwBmYXt7u+N1SheFAoxjb28vms1mx7Sz34yHUa1W4/DwMCqVSt+/3759e5LwAAYadCHVpL/bDpp/0IVYeSjK+B71U1IyzzljGKMer7Yn88B+nn4dTF8DJpNCnkshBmB61C+ArKlfAP2oX8DspdzXT+H7P4UYIDUp541RFaUt+iAUWVGOs6yodwBZkBsuJ9dCmhxr6tvAbKSQb1OIASi3otQU9a+AUalrASlT24L5lfI5WAr9oRRiAHqlnLtGVZS26I/B5IpyvGdFLWw4C3kHAAAAAJCqVqsVjUYjIiLW19djfX0954gA0rW0tNQzzUOIAQDmT7+BGYMeRgyQikHnr+12e7aBABTU3t5ex+t33nknp0gAsnH79u2eaW+//fZIy6hWq7G7u9v3b81mU18TmIo333yz7/RWqzXRcgfNP+hCrFkr0vge9VNSMq85Y1ijHq+2J/PAfp5+HUxfAyaTQp5LIQZgOtQvgGlQvwD6Ub+A2Uq9r5/C938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      "text/plain": [
       "<Figure size 9000x1200 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "30b5f8bd305b41c9b9d8c842ffdb5c1d",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Fitting stars:   0%|          | 0/8219 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
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      "text/plain": [
       "<Figure size 9000x1200 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "2c293457e7174f67a1c7dd6c1569465c",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Fitting stars:   0%|          | 0/14867 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
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      "text/plain": [
       "<Figure size 9000x1200 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
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      "text/plain": [
       "<Figure size 9000x1200 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "323397\n",
      "CPU times: user 13min 21s, sys: 14.8 s, total: 13min 36s\n",
      "Wall time: 14min 23s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "import matplotlib.pyplot as plt; import numpy as np; from astropy.modeling import models, fitting; from scipy import stats\n",
    "from astropy.stats import sigma_clipped_stats; from photutils.detection import DAOStarFinder; import warnings; import logging\n",
    "from tqdm.notebook import tqdm; from pathlib import Path; import pandas as pd; from astroquery.mast import Observations\n",
    "from astropy.io import fits; from astropy.wcs import WCS\n",
    "logger = logging.getLogger(__name__); logger.setLevel(logging.ERROR); warnings.filterwarnings(\"ignore\"); logging.getLogger('astroquery').setLevel(logging.ERROR)\n",
    "known_good_regions = [\n",
    "   {'name': 'NGC104', 'filter': 'F814W', 'exposure': [10, 100], 'index': 0}, {'name': 'NGC1851', 'filter': 'F814W', 'exposure': [10, 100], 'index': 0},     \n",
    "   {'name': 'NGC6752', 'filter': 'F814W', 'exposure': [10, 100], 'index': 0}, {'name': 'NGC6397', 'filter': 'F814W', 'exposure': [10, 100], 'index': 0},     \n",
    "   {'name': 'NGC6341', 'filter': 'F814W', 'exposure': [10, 100], 'index': 0}, {'name': 'NGC6791', 'filter': 'F814W', 'exposure': [10, 100], 'index': 0},\n",
    "   {'name': 'NGC5139', 'filter': 'F814W', 'exposure': [1, 1000], 'index': 0}, {'name': 'NGC6205', 'filter': 'F814W', 'exposure': [1, 1000], 'index': 0},\n",
    "   {'name': 'NGC5272', 'filter': 'F814W', 'exposure': [1, 1000], 'index': 0}, {'name': 'NGC5904', 'filter': 'F814W', 'exposure': [1, 1000], 'index': 0},\n",
    "   {'name': 'NGC7078', 'filter': 'F814W', 'exposure': [1, 1000], 'index': 0}, {'name': 'NGC6656', 'filter': 'F814W', 'exposure': [1, 1000], 'index': 0},\n",
    "   {'name': 'NGC6254', 'filter': 'F814W', 'exposure': [1, 1000], 'index': 0}, {'name': 'NGC6218', 'filter': 'F814W', 'exposure': [1, 1000], 'index': 0},\n",
    "   {'name': 'NGC6809', 'filter': 'F814W', 'exposure': [1, 1000], 'index': 0}, {'name': 'NGC6838', 'filter': 'F814W', 'exposure': [1, 1000], 'index': 0},\n",
    "   {'name': 'NGC362', 'filter': 'F814W', 'exposure': [1, 1000], 'index': 0}, {'name': 'NGC6388', 'filter': 'F814W', 'exposure': [1, 1000], 'index': 0},              \n",
    "   {'name': 'NGC6981', 'filter': 'F814W', 'exposure': [1, 1000], 'index': 0}, {'name': 'NGC7099', 'filter': 'F814W', 'exposure': [1, 1000], 'index': 0}\n",
    "]\n",
    "all_results = []; all_alpha_values = []; all_gamma_values = []; all_fwhm_values = []; alpha_data_per_object = []; labels_for_box = []\n",
    "for region in tqdm(known_good_regions, desc=\"Processing regions\"):\n",
    "    try:\n",
    "        data, wcs, target = download_hubble_flt_data(region);\n",
    "        results = analyze_hubble_field(data, target)\n",
    "        if results:\n",
    "            result_summary = {'name': region['name'], 'star_count': results['star_count'], 'alpha_median': np.median(results['alpha_values']), 'alpha_mean': np.mean(results['alpha_values']), 'alpha_std': np.std(results['alpha_values']), 'gamma_median': np.median(results['gamma_values']), 'gamma_mean': np.mean(results['gamma_values']), 'gamma_std': np.std(results['gamma_values']), 'fwhm_median': np.median(results['fwhm_values']), 'fwhm_mean': np.mean(results['fwhm_values']), 'fwhm_std': np.std(results['fwhm_values'])}\n",
    "            all_results.append(result_summary); all_alpha_values.extend(results['alpha_values']); all_gamma_values.extend(results['gamma_values'])\n",
    "            all_fwhm_values.extend(results['fwhm_values']); alpha_data_per_object.append(results['alpha_values']); labels_for_box.append(region['name'])\n",
    "    except Exception as e: pass\n",
    "create_histograms(np.array(all_alpha_values), np.array(all_gamma_values), np.array(all_fwhm_values), \"Averaged by regions\")\n",
    "print(len(all_alpha_values))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "966e56ac-1a57-4760-a0c4-548e9f61a47c",
   "metadata": {},
   "source": [
    "A clear peak at 1.5 is visible in the alpha (beta) parameter, and neighboring diagnostics show that this is the system operating at the limit of discretization and resolution."
   ]
  }
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